Your system may be trying to tell you the HD is in trouble. Please look over Gray progress bar appears under Apple logo during startup
You can also try rebooting again, when you hear the startup tone hold down the Option key and choose your internal HD. If it boots OK then navigate to System Preferences - Startup Disk and make sure the internal HD is selected and then restart again.
If it still restarts in Safe Mode then run Apple Hardware Test per the instructions in your owners manual. If you no longer have the owners manual then click Support in the upper right of this page then click Manuals and navigate until you locate your manual. Run AHT in Extended Mode, if no errors come up after the first pass you should run it another 2-3 times. Each pass will take about 30-60 minutes.
Well, I have done the AHT twice, once in Extended Mode - and it says all clear. I will try again.
But it does seem like the HD is okay. And even it was in trouble, that should not affect booting from the system cd, which doesn't work either, right?
Normal boot up always ends in the blue screen loop unless I go into safe mode.