i really like the look of that case, why haven't i seen it before...
(probably costs alot too >.<)
your case looks fine, that psu that it came with appears to have reviewed pretty well too, and also has a 5yr warranty. with that said, i don't know how much it could've degraded over time.
you could upgrade the cpu though. for your particular board, it looks like the best cpu you could upgrade to is a x4 965 (with a bios update).
http://www.gigabyte.com/support-downloads/cpu-support-popup.aspx?pid=2690
if you upgrade to another cpu for that board you'll still be able to use your cooler, if you change you board out for say an lga1156 or 1366, you might be able to use it on those with an adapter if zalman made any, since those sockets aren't listed on the compatibility list there.
ram you could upgrade too. add 2 more gigs, or (since it sounds like you could be havin some problems with those), get a whole new set (2x2gb).
gfx card, you could upgrade too, just depends on how much you wanna spend.