If you can remove the HDD and put it in an external enclosure with a USB cable you should be able to access the files from any computer with a USB port. Or, if you're sure its a faulty PSU you can find a temporary substitute.
Most data loss can be resolved by data recovery software, I happen to know a freeware and I have used it to retrieve lost data before, it is very powerful and useful: http://download.cnet.com/iCare-Data-Recovery-Free/3000-2248_4-75628752.html u can easliy restore lost files with only a few clicks and some patients in case the files are large.