I'm running mine on a Core™2 Duo E6750 and an 8800 GT 512MB VRAM with some decent detail, a LONG draw distance with no problems. I think you'd have to turn off some detail, but it should run OK.
The minimum specs are:
2.4GH P4, 1 Gig of RAM and an NVidia 6800 with 256MB VRAM.
The recommended specs are:
Dual core, 2 Gigs of RAM and a video card (including the 7600 series) with 512MB RAM.
As you said, you fall in between those. So, I did a bit more digging as I eat lunch at my desk.
Here's a link on the Fallout 3 forum regarding system specs:http://www.bethsoft.com/bgsforums/index.php?showtopic=915772&st=0&p=13292864&#entry13292864
You can see your 7600 GT card should be able to run FO3 with some settings turned off.As a side note, Empire TW isn't as smooth on my system as Fallout 3 - and that's without the crashing problem with TW.