Hello, the crashing isn't normal.
One way to test is to Safe Boot from the HD, (holding Shift key down at bootup), run Disk Utility in Applications>Utilities, then highlight your drive, click on Repair Permissions, Test for problem in Safe Mode...
PS. Safe boot may stay on the gray radian for a long time, let it go, it's trying to repair the Hard Drive
Reboot, test again.
If it only does it in Regular Boot, then it could be some hardware problem like Video card, (Quartz is turned off in Safe Mode), or Airport, or some USB or Firewire device, or 3rd party add-on, Check System Preferences>Accounts (Users & Groups in later OSX versions)>Login Items window to see if it or something relevant is listed.
Check the System Preferences>Other Row, for 3rd party Pref Panes.
Also look in these if they exist, some are invisible...
Quite a few USB 2.0 eMacs with 1.0 and 1.25Ghz processors had a near-fatal logic board problem that is today probably not worth fixing. Crashing shortly after startup or as soon as you launched any program was one symptom of the bad boards.
The ones with bad logic boards were in these serial number ranges:
- G8412xxxxxx- G8520xxxxxx
- YM412xxxxxx - YM520xxxxxx
- VM440xxxxxx - VM516xxxxxx
There was an repair extension program in place to fix these at no cost to the owner but the program expired nearly three yeas ago.
This article shows where to find the serial number:
If the serial number starts with "R" or "RM" the computer is a factory refurb and the above list wil not help.
You can open the RAM door on the bottom of the case to check for the problem---leaking capacitors. This image shows what "bad caps" look like:
Note the brown goo on top of the capacitors.
Not completely diagnostic because caps other than those visible through the RAM door could be the bad ones. Nevertheless, if you see what's in those images, I think you are done unless you can extract the logic board, desolder a bunch most of the capacitors, find new ones with the right specs, solder new ones in without frying them with the solder gun.....well, you get the picture. It's not a DIY fix.