Although some cases do not require motherboard standoffs because they are built-in, are they required in the new case and if so, did you install them?

To be honest with you, I'm not even sure what that is. :/

Standoffs are short risers that keep the motherboard from touching the case. If you screwed the motherboard directly to the case without using these separators, the motherboard will short to the case and, of course, won't start up.

They usually come with the case.

Hmm, I see what you mean. I simply placed my motherboard in place of the one that was within the case. Would it be possible that the fit is not right and therefore causing the short?

Here is a sample of typical motherboard standoffs:

You also need to make sure the motherboard mounting points are the same between the two boards. If you placed the new one in place of the old one without regard for the standoff placement, that could also short the board. This would be especially true if you replaced a standard ATX board with a Micro ATX board or vice versa.

That sounds highly probable, as the case is certainly ATX and not Micro ATX. I even had to forgo some screws in order to have it sit in place.

I gave up with the new case and moved back to the old one but the problem persists :/

Again, the fans run perfectly fine, but I can't get video output from either of my GPUS. Did I damage my mobo?

Any beep codes?
It's a long shot, but try swapping out the video cable. you never know... It could have gone bad coincidentally.
Try pulling out the video card and reinsert it. it could have been bumped during the process.

At this point please give us the make and model of your PC components including the power supply.

Not getting any beep sounds. Just a general high pitched electrical current type sound. (Like when a TV starts up).

I am using:
ASUS M2N68-la motherboard
Intel Athlon X2 3.2 Ghz processor
3 GB RAM across two sticks
GIGABYTE Radeon HD 5750 1GB GPU
Acepower 450W PSU

And I'm not too sure on how to detail the cases exactly.The one I am currently using is an ASUS that has served me well since I initially put the computer together.

I have tried removing the graphics card altogether, but my integrated chip, a Nvidia 6150, won't offer any image either.

I've also tried using two separate video cables with no luck. I have an HDMI I could try, but have hesitated since the cord is short and I will have to place the tower directly next to my TV.

If you shorted the motherboard, something might have been damaged although you can often get away with no damage but perhaps you were unlucky. Also, if you weren't careful to avoid static electricity when handling the parts, one or more parts could have been damaged. As a side issue, if you separated the heatsink from the CPU, you should always clean off the old thermal compound and apply fresh compound.

Do you have access to any spare parts to test with? Could you start with the power supply?

I can swap out the PSU, CPU and remove the video card. I'll get right on it after lunch and see what happens.

Do the CPU last because it's the most disruptive next to the motherboard itself. Also, try one RAM module at a time, each in turn.

It can normally be determined whether a motherboard mounting hole should be grounded, (or even used), by looking for the solder "lands" around it. These would be on the top side of the board, (NOT the circuit printed side), and are usually a ring of solder, "dots" around the hole.

If a mounting hole doesn't have these lands, skip it. I have seen cases that suppy a plastic stand off, and I'm certain that would be its purpose, to use for a mobo hole that requires insulation, rather than grounding.

Changed everything step by step, checked RAM and still no luck.

It's still not clear to me whether the motherboard standoffs are properly installed.

Had a friend come by who has much more experience, he made sure everything was set-up properly, in both cases and we still got no display. I opted to buy a new mobo and we are going to try it out tonight. I wanted one with Crossfire anyways.

Got the new Mobo in. Working great. Was forced to reformat my drive to get it all working properly though.