before you replace the PSU you might want to look into the overheating option. encoding or transcoding video is a very intensive process and it’s very possible it’s heat and not power that is causing the reboots.
the reason i say this is beacuse PSU issues tend to be more random, and from you rstatements it seems pretty consistent that dvd processing causes shutdowns.
can you check temps in your BIOS or use a 3rd party program like everest home edition to check temps inside your case?
you said your fan has been loud lately…can you check to make sure that all fans inside your case are properly spinning and working?
sometimes the solution is something as simple as blowing out the dust and gunk that is clogging the fans and vents with a can of compressed air. if this is your problem, this will probably reduce the heat a LOT. Even if this is not your problem, it’s never a bad idea to keep the inside of your case clean and gunk free!
like i said, i’m not discounting the PSU suggestion, but checking for heat problems is less expensive and invasive and it probably a better first step. if you clean out the gunk and the temps measure normal then by all means try to replace the PSU.