Newer card in an older machine

So I've been trying to inject some new gaming performance into my older machine with a new graphics card but I've encountered some difficulties.

First my particulars.

Motherboard: XFX Nforce 680i SLI LT
CPU: Core Duo Quad Q6600 2.4 Ghz
Ram: 8gb of DDR 2 (4 sticks of 2)
Power Supply: 650 Watts
Old Graphics cards: 2 x EVGA GeForce 8600 GT (SLI)
New Graphics Card: XFX HD 7870 Double Dissipation Edition

So I swapped out cards no problem and the machine booted fine at first but then quickly the monitor lost a signal form the GPU. After the initial failure could not get the monitor to get a signal from the GPU. All the fans and lights for the computer came on (the GPU powered up) but the monitor wasn't recieving a signal from the GPU.

So I removed the card from the primary slot (the one it's supposed to be in for single card config) and moved to the secondary slot. Computer booted fine and everything seemed to work great. Updated motherboard and GPU drivers. Would like to get the card working in slot 1 though (much better for air flow and space management inside the casing). Tried to put it back into slot 1 and the same thing as before happened (worked for a moment then dead). Put it back in slot 2 and carried on.

Over the next few days, the computer would ranomly freeze, re-boot or the monitor would lose its signal from the GPU. This would happen infrequently at first but then more often as time went on.

Tried to replace the side panel on the casing and the computer immediatly crashes when the panel is slid into postion. Cannot boot computer with side panel on (!).

Suspected a short or something loose somewhere. Pulled just about everything out of the computer and re-run the wires and cables. Re-seated all components. No visable sign of damage anywhere. No leaking or bulging capacitors.

Computer now boots and runs okay. But will still randomly freeze, re-boot or monitor looses signal from time to time. Can happen anytime. Have played 3D games for hours straight with no problems but have also crashed just sitting at the desktop.

If computer is jostled or moved or if the side panel is slid into positon then it will crash. The computer sits against the floor and if it's moved too close to the back wall it crashes (!). So at this point I start suspecting airflow and heat is an issue.

Also, I noted that crashes happen much more frequently when all of the case cooling fans are connected to the PSU. Right now I've got the case fans unplugged (on account of the side panel being removed). But if I actually power up all of my case cooling fans (I have 3 inlet and 1 outlet fan) then the computer will be very reluctant to boot up and will crash in short order.

I had thought of buying a more powerful power suppy, but in retrospect I think 650 should be enough.

Finally, the new graphics card does technically fit into the older motherboard. however, it certainly seems to strain the PCI-E slot. The new card weighs a tonne when compared with the older cards. I can visibly see the card pulling down and leaning slightly. Could be shorting out the PCI-E slot (especially slot 1)?

So here's what I suspect could be the problem:

A) short or loose connection
B) underpowered power supply (not putting out 650 watts?)
C) Heat or airflow issue
D) General incompatibilty and/or instability with this older board and newer card.

So any hints or suggestions about what to do next would be helpful.

Thanks.