Well my first thought is yes you should be able to. How old is your PSU? You might want to consider buying a new PSU. I have a 20a PSU currently running a x1800xt w/an AMD 3200+, which would consume more power than the e6400 that you have. The x1800xt consumes about 103w at full load. By the link below, you'd be consuming 99w (256mb) or 109w at full load, so I'm betting you'd be okay. But I'd seriously consider upgrading your PSU. http://www.atomicmpc.com.au/forums.asp?s=2&c=7&t=9354
Edit: I forgot to add that I'm using a Raidmax 420w PSU, which isn't nearly as good as yours. If you look at my sig. you will see the rest of my current PC.
If what I've read in a few places is correct (googled x1900xt) your card will require 30amps on the 12v rail, which sounds about right. I would definitely get an upgrade.
There are some pretty obvious recommendations that a lot of people make, but you'll just have to figure out what's in your budget. Here's a link to a xtreme systems page that puts psu into tiers, Tom's wiki is a bit better imo, but I can't find it for some reason: http://www.xtremesystems.org/forums/showthread.php?t=10...
Do your best to get one in the top three, or better, the top two. You'll probably need to get something in the range of 500 watts. Not that watts are the most important factor, but simply a guide. Most people, including me, would recommend Antec, Seasonic, Corsair, PC Power and Cooling. I have an enermax, which I love, but their build quality has gone downhill in the last couple of years (or so i've been told). Good luck.