I don't have trouble like this with my powerbook and Tiger, though 10.4 seems subjectively to be *much* buggier than 10.3 (I have problems with disks mounting, the DVD player sometimes failing to recognise playable disks, and spotlight failing to index some things are know are present).
Try opening the 'utilities' folder (go to finder, then press 'apple-shift-U'), then try the running "Console".
The 'system.log' is as the previous poster suggested /var/log/system.log, and it may contain some helpful hints as to what is wrong. Also worth looking at are console.log and the crash reporter logs.
Also, if you can start up from the install DVD, you can run Disk Utility (use the menu bar to select the program before starting an actual installation). This may be able to repair any disk problems that you might have. If you think the OS files are damaged, then try re-installing Tiger as an 'upgrade' rather than a clean install, and only if this doesn't work try doing a completely clean install. It's worth adding that I've never needed to do either of these in the time I've been using OSX (about 3 years now).
Hope this helps.
:: Mark (Mac tech support
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