Didn't Lords of the Realm III come out? Never tried it but it definitely looked like it had some castle siege warfare.
The game that had by far the best sieges I've ever experience was Rome Total War. It may run on your laptop but definitely try the demo first.
Rome is a little behind Medieval but it's still all the same stuff, siege weapons and towers, archers, infantry, GIANT castles, and so on. I played one map, Rome, with myself and one computer ally as Rome's defenders. 2 enemy computer AI's as the attackers. Armies were randomized by the computer so there's not much micromanagement, you get what you get and once your troops are gone, your'e done. You can also set any of your troops to be controlled by the AI, so if you only want to control your calvary, you can set everyone else to AI-control. Or just control everyone.. however you like it, you still have an AI buddy who is fighting beside you to defend Rome.
Rome itself is HUGE. Giant walls surround the city itself, so it's a tough battle getting in. You'll see your AI partner position his troops around Rome, keeping a few back at the center of the city which is where you need to get to conquer it.
I put all my archers on the walls themselves, couple of seige weapons scattered around the city (which I always set to AI-control) and left my general and his troops in the center of the city.
From there, you'll experience thousands of enemy troops marching on Rome. They'll be firing catapults, moving siege towers to your walls and keeping their archers back to help counter yours on the wall. When their siege tower reaches the wall, you'll see enemy troops start coming up and at this point, you either stand your ground on the wall with your centurions and other infantry, or you start pulling them back for more ofa guerilla warfare in the city streets themselves. (The city streets are tiny and troops have to bunch up together to get through, plenty of good ambush points.) I usually put about 30 infantry on the wall to hold them off while I regroup my other troops. They'll eventually over power your infantry and start coming down the walls into the city itself, and from there it's all or nothing. They make their way for the city center to conquer you fighting your troops along the way.
All at the same time, your AI ally has been holding up the other side of Rome against the other enemy who's been trying to breach those walls. He's been doing a hell of a job as the barbarians still haven't been able to get through his forces. (The map Rome really is that big.)
If you play your cards right, you can take the barbarians out in urban warfare on the city streets, but if you're careless, they'll cut through you like butter. Your ally will send what he can to the city center to help you, but then his remaining forces end up getting overwhelmed and now you're being attacked on all sides.
Needless to say, the real-time Sieges in Rome Total War are by far the best I have ever experienced in a video game, ever. The fact that you can mix and match teams - so you're not "alone" in defending the huge castle, is what makes it all the more fun.
Since Medieval Total War II came after Rome, I can only imagine they made the sieges all the better. (But as with you, my PC would never be able to pull it off.)
Another game - Besieger. It's RTS but it comes with a few prebuilt Siege maps. You can play as attacker or defender. The computer brings ladders and everything to your castle and tries to take it over. Usually about 40 units per side. Standard siege, but all real-time.
A little older (1700s I think) Cossacks is RTS, but comes with prebuilt maps as well. Fun as hell. If you play as defender you have to try and hold off against the advancing enemy infantry and their non-stop cannons that are pounding your town. The unit numbers are often in the thousands, so it's a big battle that can go on for quite a while. A lot of the maps as the defender you're outnumbered, which makes it all the more fun to try and hold off against the attack.
Finally, my current favorite PC game, Rise & Fall Civilizations at War. I wrote a pretty in-depth experience of it in the trading forum of one of my games, but to make it short, it's a real-time strategy game (you can zoom in as close as you want to the battle so you're right there in it or as far back out to where they look like ants) that has battles in the thousands. There's some micromanagement in the regular skirmishes, but the AI builds up good sized walls which you'll have to take down or go over with ladders.
All kinds of siege equipment from battering rams, siege towers, ladders, ballistas, and more. Best part of the game - you can be the hero. You can control your hero directly in third person view, using standard first person controls to control him. (WSAD, left mouse to attack, etc) Joining your troops on the front lines is a great experience. The enemy has their heroes as well. Whenever we get huge battles going (couple thousands infantry battling eachother in the middle of the map with catapults and archers blasting everybody from the distance) I always look for the enemy hero and meet him in the battlefield. Damn fun!
The map editor in Rise & Fall you can make any kind of siege you can dream of. I built a map where I was King of the castle - so you control your hero, only ONE guy, Julius Ceaser.. It's in third person view. Your ally, the Egyptians, have about 200 troops and Cleopatra backing you up. Archers are scattered thinly across the walls, 2 catapults inside the castle, a few healers, and a variety of infantry soldiers stationed across the castle.
The enemy, the Persians, have approximately 3,000 troops. (Yes you're outnumbered 15 to 1!) Their troops however, are mostly light infantry and they have no archers. They have 4 catapults, 4 siege towers, 2 battering rams and a dozen ladder teams.
With your hero, you can choose between hand to hand combat or bow and arrow. So as you see the enemy slowing marching towards your castle you can usually pick a few hundred of them off before the siege towers and ladders are in place. (Plus Cleopatra and her archers are letting them have it too.) The catapults will usually end up taking out a block of the wall before their siege towers or ladders are in place, so they'll try to come in through that tiny gap. Your egyptian infantry allies will battle them at the opening while the egyptian archers keep firing from atop the walls. (Although it's funny as hell watching the catapults take out the part of the wall where some of the archers were stationed!) Cleopatra is bipolar you never know what she's going to do. Sometimes she'll stay on top of the walls and keep firing arrows, other times she'll go down to the center castle and fight hand to hand.. mostly she stays back with her bow and arrow though.
If you play very cautiously (if you die, game over) and do your best you can win with all of your allies dead. If you sit back and watch your Egyptian allies try to defend the castle by themselves (which can be fun also) you'll be completely overwhelmed by Persian troops and lose. I stayed on top of the wall during one test and watched them take down the wall, come through the gap, kill all of my allied troops, climb the ladders to the top, battle their way through the archers and infantry stationed on the wall, until they got to the end where me and Cleopatra where. Cleopatra held her own taking out at least 20 Persians before they hacked her down, while I took out another 40. In the end, we lost..
That's just one exmaple of a siege map I made. Whatever you can think of, can be done in Rise and Fall. The walls are life-size, catapults and battering rams are huge, the battles are in the thousands, and you get to control your own character if you want. To this day, it remains my favorite PC game of all time.. highly suggest you check it out!
Ah well, so much for "short"!