Hi, Lenny.
Normal Mode = Windows + 3rd Party Drivers
Safe Mode = Windows + Microsoft only Drivers
In Safe Mode, only the most basic and safest drivers are loaded. This is why your screen looks all funny in Safe Mode, because the normal video driver isn't being loaded. Since you're not crashing in Safe Mode, but are in Normal Mode, we can conclude that it might be a 3rd party driver that is causing the problem.
Set your PC up to use the "Small Memory Dump" files. These are also called minidumps. [
Here are some instructions.] Then try normal mode again. Each time you have a BSOD your PC will create a minidump. They will be located in the C:\Windows\minidump folder.
Once you have 3 to 5 minidumps, upload them to a public server and post the link here so they can be reviewed by others. You can zip them up if you like. Sometimes we can point to an exact driver that is causing the BSODs and help you fix it.