I'm having trouble getting my PC to post, when the PC boots, the fans spin and the lights come on, but it reboots shortly after, sometimes I get past the bios post screen, other times I don't, also it may get stuck in a rebooting cycle if I let it sleep. Also the picture on the monitor goes green or I get a series of white lines or dots at the top left of the screen if it manages to get to the windows 7 log on. It may also give a series of short beeps and refuse to boot.

I have tried the following:
I recently changed the PSU from a silver stone rider to a a EVGA SuperNOVA G2 Gold 650W but that only fixed the issue briefly, I thought it was my GPU so I recently RMA'd my MSI 380 and got a Sapphire 480. This worked for a bit over a week, but now it's having the same issues again. I tried resetting the bios to defaults and changing it again but same results. I would like to switch PCI slots and see if that makes a difference but my GPU won't fit in that second slot as the front panel headers get in the way, so do some of the board's capacitors. I tried removing and swapping the RAM sticks with the same results (I don't think it's the RAM). I suspect the board is shorting out or the PCI slot is faulty because it I move the GPU around in that slot, it may/may not work (it's defiantly clipped in). I've noticed that the GPUs will not read the back panel of the case to screw in unless I bend or push the back of the case towards the GPU.
The PC will boot fine if I don't plug a GPU in (it consistently posts fine without one), or it'll work for a week or more if I plug a new GPU in, this pc was running fine since 2013, and the old GPU (AMD 380) was running for almost a year and a half before issues started). The PC seems pretty stable once it does start windows and I don't see any errors or warnings in the event viewer. I can play a game like Titanfall 2 at 1440p with no obvious GPU errors (I actually just finished the campaign today) and most games run fine.
Any idea's on what else I can try? I was going to move the internal parts to another case and see if that helps but haven't done that yet (in case something is touching and shorting, or the case is somehow pulling the GPU out of the PCI slot). I suspect the case is at fault or the motherboard has a damaged PCI slot, or there's a short somewhere.
Here are the stats:
Operating System
Windows 7 Home Premium 64-bit SP1
Intel Core i5 3470 @ 3.20GHz 52 C
Ivy Bridge 22nm Technology
8.00GB Dual-Channel DDR3 @ 665MHz (9-9-9-24)
Gigabyte Technology Co. Ltd. B75M-D3H (Intel Core i5-3470 CPU @ 3.20GHz) 28 C
ASUS MG279 (2560x1440@144Hz)
8192MB ATI Radeon RX 480 Graphics (Sapphire/PCPartner) 48 C
232GB Crucial CT250BX100SSD1 ATA Device (SSD) 30 C
3726GB Western Digital WDC WD40EZRZ-00WN9B0 ATA Device (SATA) 33 C
29GB Kingston DataTraveler 3.0 USB Device (USB)
57GB Kingston DataTraveler 3.0 USB Device (USB)
Optical Drives
DTSOFT Virtual CdRom Device
Sound Blaster E5
The case is a Thermaltake V4 black edition and the PSU is a EVGA SuperNOVA G2 Gold 650W, I don't want to buy a new motherboard yet if I can help it because I'm waiting to see how Ryzen/Kaby Lake pan out first.

The mobo can supposedly do crossfire, but I don't know how your supposed to fit a gpu in there, the AMD 480 interferes with front panel headers. Otherwise I'm doing this wrong somehow.

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I did notice that it keeps changing the bios settings, I had the PCI slot set as main display and integrated graphics as disabled or auto. But it's changed the main display to auto after a reboot.