I've had similar problem to yours. I was using a 256MB 1.42Ghz mac mini with Tiger installed. It seems that the mac keeps on crashing or it never boots (stucked in the booting screen). I've found out that the hard disc died (it shows RED aka Failure when you boot from the DVD).

So , I had to buy a 100GB 2.5" Hard Disc and replace it. Opening was pain in the butt. Then , I replaced the RAM with 512MB of Stick and its running okay.

It might be the hard disk. Check Disk Utilities (its in the Utilities folder) , make sure the SMART Status is okay. Otherwise its your HDD that is giving you the problem