Is this the desktop? http://i.walmart.com/i/rb/0009980294238.pdf
It seems it only has a 220w power supply. You're going to want to upgrade it if you get a new video card.
It also seems like the tower might be too small for a normal higher end video card according to this thread - http://www.sevenforums.com/graphic-cards/170512-new-computer-question.html.
They recommend a low profile video card. The 6670 should be able to run SWTOR on low-medium settings. They have the low profile version on newegg. http://www.newegg.com/Product/ProductList.aspx?Submit=ENE&DEPA=0&Order=BESTMATCH&N=100006662&isNodeId=1&Description=6670+low+profile&x=0&y=0.
I didn't see any low profile 6770s.
If that card can fit, I would purchase a 6670 and at a 400W+ power supply. Both should be well under your limit.
Edit - Forgot to mention that even though the 6670 is a low profile card. It's still quite large. They have the dimensions listed on newegg. I would get out a tape measure to make sure it will fit inside your case.