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>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...
I have read up about kernal panic. I have done the above and will see if it crashes ~ this is a Safari related event, I have Menu Meter running, when the activity monitor I have starts spiking at 100%, usually when I am trying to do something like sign in, or for instance, right now. As I watch the virtual memory number creeps up, its 1 Gg now. It shows my HD to be 55.89 Gb with 42.49 utilized. This is a iMac PPC. updated to Tiger with, I believe, some additional memory. I do not have a Airport, or any additional device and am using new Mac keyboard and original mouse and speakers. It could just be the internet and the memory that has shown as a new problem because up until a few weeks ago I used to reset Safari several times a day. . .then NYT changed their paywall : (.iMac, Mac OS X (10.4.11)
Might try a different browser...
TenFourFox is the most up to date browser for our PPCs, they even have G4 & G5 optimized versions...
SeaMonkey seems pretty fast also, with many options...