Inspiron 8600 HELP PLEASE!!

I have posted here before with amazing results so I am again asking for your help. I have an Inspiron that recently started acting up. The LCD would dim at odd times so after assessing that the screen was good, I ran diagnostics that came back with a failing mobo. I replaced it and all was going well for a few days until today. Now when I go to boot up, nothing shows up on the screen and then I hear two beeps. I hear the CD drive going through its normal start up sounds and the sound of the hard drive, but no Dell logo on the screen, nothing. Just the two beeps. Anybody? I am frustrated beyond belief at this point. I consider myself pretty adept at handling any issue as to component replacement, I just need to know what is going on. I have no warranty left. Thanks for any light you can shed...

 

Beep codes
http://www.amptron.com/html/bios.beepcodes.html
AMI is the only one that shows two beeps and it says bad memory.
If you have two memory chips in, remove one and boot up. Granted, the computer will be noticeably slower on half the memory. If you hear no problems, then the other chip might be bad.

 

so, I did as you asked and removed one at a time the two memory modules to reboot. After the F1 error message about the memory change the computer booted normally. Both times. Then, with one module in at a time I ran the diagnostics cd checking each moduloe seperately. Again both passed all the tests. So I put both back in and tried to reboot. Again, the computer made to typical sounds but with no Dell logo appearing, nothing at all on the screen and again the two beeps. As the computer had been sitting overnight and off, I wonder if the time it took to run the tests, about half an hour, if that was enough time to potentially heat up a sensitive area of the computer that now wants to malfunction. Not sure. My fans run fine, so I think I'm grabbing at straws. I am at a loss as to what this could be. Last night as I was running the diag cd on the whole system, the display started looking add. Some words appearing smeared or digitized, though otherwise a normal screen. Then I pressed the pin that shuts the screen off when you close the lid and released it thinking that would clear the screen, but instead it wiped it completely black not to come back. I rebooted and that's when the cycle of behavior repeated itself. Not sure what else to do. In spite of the two system beeps, as the two modules check out I don't think it's the memory. Thanks again for any input!