I see no good solution for your situation if you don't have the cd's anymore. wma's suck, I'd never ever use them. For me, there are only two options: lossless, or mp3. If you go lossless, just use FLAC files or APE or something like that, and if you want compressed files, use mp3 (LAME encode).
dbpoweramp is a brilliant piece of software. As a last minute rescue, go on the original computer and use dbpoweramp to convert all those wma's to mp3, and transfer those to the new computer. You will lose a lot of quality in the conversion, but that's all I can think of. You can also use another software to do it, but dbp is really easy to use and amazing.
Or, you can download the songs pre-ripped from any of several online places. That would probably be the better option, but it may cost you a little!