Well, as far as using a multimeter goes, I'm sure there's a way to at least test the PSU. I'm PC savvy but not multimeter savvy - I just use them to test old batteries. I have enough computer junk laying around that if a component goes bad, I just swap out with a known good one. It's a pretty safe bet that if no lights, fans or anything else show any signs of life that you have a bad PSU. The PSU should have an exhaust fan facing the rear - see if it spins up.
If you're looking to pick up a new PSU, don't go for an exact replacement. Newegg.com has great deals on aftermarket PC components...you should be able to grab a respectable PSU for 20-30 bucks. They can cost well over $100 for a high end model but an older PC won't need such a beast. I've had good luck with both Logisys and Raidmax for cheap, decent PSU's. Both of these are less than $30 shipped.
http://www.newegg.com/Product/Product.aspx?Item=N82E16817170016http://www.newegg.com/Product/Product.aspx?Item=N82E16817152019Even if you fried your motherboard, you can get a new, lower cost one for around 50-60 bucks. Unless I'm mistaken, your PC has a Core 2 Duo processor - that's worth salvaging in my book. Here's a cheap solution - $45:
http://www.newegg.com/Product/Product.aspx?Item=N82E16813130234Obviously, I don't know your system specs but some diligent searching at newegg.com can yield some pretty sweet deals. You can get away with spending ~$100 if both PSU and motherboard are fried and have a fully restored system. That $100 figure applies if you do the work yourself. Don't get raped by the Geek Squad - the only thing they do well is overcharge...
Most likely, you just have a bad PSU. Somewhat likely, it took your motherboard with it. DVD & hard drive are probably OK although you could very well have lost or corrupted data. Your RAM is probably OK either way. RAM can be tested easily...open source app called memtest86 is well suited to that task. Good luck and if there's anything I might be able to answer, lemme know.