Athlon II X4 620 Quad Core 2.6ghz cpu
8gb DDR 3 Ram
500gb SATA HD
Asus GTX 650 1gb GPU
IDE DVD-RW
Trust 540 Watt PSU
OK, so we've got an AMD system with a suspected fried m/board.
The CPU is AM3 (meaning it'll typically fit an AM2+ or AM3 or AM3+ m/board but check the spec per board), but you have DDR3 RAM, so I think that means you're looking at an AM3/AM3+ board (AM2 and AM2+ were DDR2 only, AM3 and up are DDR3 only).
The PSU, GPU, SATA HD should be no issue with most anything, and many but not all AM3 boards keep at least one IDE connector for optical drives.
You don't say if the RAM you have is 4 DIMMs of 2Gb each or 2x 4Gb (or even 1x8Gb) so I'll assume 4x2Gb, meaning you'll need a mboard with at least 4 DIMM slots.
It's a nice low wattage CPU (45W TDP) so probably runs a very small heatsink but doesn't make any high wattage demands of a m/board.
The case, will it fit an ATX or just a uATX (uATX is physically smaller) board?
No point in someone volunteering an ATX board if it won't fit in your case

I'm guessing from the "cool-running" CPU that it's a small case so would suspect uATX.
And no mention of other cards, so I guess it won't matter how many PCI-E 2 x16 or better slots there are, you just want the one free high speed slot for the GPU card.
And given your posts about swapping bits and pieces over to test the PSU etc, I take it you'd be happy to try swapping the mboard yourself (remove and fit, reseating the CPU and heatsink and RAM, swapping connectors etc).
Given this is Windows world, you'll probably fall foul of Microsoft's anti-piracy checks on a m/board swap, but if so you just have to ring them on the telephone number that shows up and tell them, absolutely honestly, that the m/board died and you've replaced it and no, this isn't a 2nd machine running the same copy of Windows but the same machine with a m/board swap.
So, according to my tired old brain, the question is has anyone got a uATX (to be safe) AM3/AM3+ m/board with both IDE and SATA, and 2 or 4 DIMM DDR3 slots lying around spare?
Something perhaps like
http://www.tekheads.co.uk/product/A...-AM3-IDESATA-Micro-ATX-Motherboard_43812.html
(Dunno how good a board that is but it came up pretty quick on a search for something with the right sort of spec).
I'll ask around a few geek mates ... see if anything comes up...
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T