My PC has started getting:

KERNEL_DATA_INPAGE_ERROR
STOP: 0x0000007A (0xC0578D08, 0xC0000185, 0x53DB28C0, 0xAF1A1000)

This error is sporadic and random.

I am *NOT* using a paging file since I have 4 gigs of RAM so the PAGING ERROR pages don't apply.

Alienware technical support is trying to tell me to run my system without any Antivirus program and that will fix the error, but to me that sounds like terrible advice.

Any ideas?

Try using Check disk by using this guide on how to use it :

http://www.maximumpcguides.com/how-...

This error could be either a hardware error or by corrupted windows files.
Most likely it has something to do with the windows files and may be corrected by using CheckDisk.