Seemingly random failure to POST on old system

[Malalkin]

So it seems pretty random, but last week my computer crashed out of the blue with just a checkerboard pattern of static on the screen (everything frozen).  When I tried to reboot, it wouldn't POST.  I played around with some wires, moved the memory to the second memory channel, checked that the CPU cooler was mounted correctly and nothing changed, but then I removed the DVD drive and it started working again for a while.  I was able to run it for 3 days straight without rebooting and there were no issues.  I thought "maybe the DVD drive is dead?".  To save wear&tear when I'm just number-crunching, I unplug the 2 SATA hard drives and just boot off a USB drive.  When I unplugged the SATA disks from power and SATA, it wouldn't POST again. Cleared CMOS: no change.

 

I managed to get a POST by unplugging the VGA cable from the back.  It kind-of booted, but couldn't find an operating system (which usually happens because I have to change BIOS options).  I ctrl+alt+deleted and dropped into the BIOS menu where things got kind of strange: it worked for about 5 seconds and then locked up with another checkerboard static pattern on the screen, this time the system speaker emitting a constant 'beeeeeep' (no beep code, just a solid beep).  I hit the reset button again and no POST. 

 

Feeling defeated, I reconnect all the SATA drives and power it on 'just to see' and it works just fine. 

 

I'm thinking maybe PSU, but if that were the case how could it stay stable for 3 days straight?  This system has worked without issues since 2010 and nothing has changed on it recently to cause this.  Any suggestions?

 

EDIT:

system specs:

AMD Phenom II X3

M4A785 motherboard (onboard graphics)

4GB DDR2 at 800mhz

2x SATA hard drives + 1x IDE

EVGA 500W bronze PSU