Pics? Bolts touching a piece of PCB doesn't exactly mean there was any kind of short, but there is no way to be certain if the bolts are or aren't causing a problem without visual confirmation.
Generally you would want some sort of gasket or washer between the PCB and bolts to avoid the bolts damaging the PBC when tightening and loosening them. Realistically, even if you did dig the bolts into the ground plane, I don't think that alone would cause an issue unless it was in direct contact with another component that had a different electrical charge to it.
One thing you could try and look at when booting is the keyboard. Generally if the computer is making it to POST you will see the keyboard indicator lights (caps, scroll, number lock) will flash and perhaps turn on the number lock light depending on your BIOS settings. If this is happening then perhaps there is an issue occurring outside of the computer itself. Plugging into the wrong output, loose connection between the cable and the monitor, or something else along those lines could disrupt the video signal.
If it is not actually getting to POST then there maybe be another issue. Making sure to reseat the card and all of the power connectors would be a good place to start. Also check the motherboard power connections to be certain they are secured down. If any of these came loose then it would starve the machine of power, causing boot issues. If none of this works out then try going back to the old card. If the machine boots up fine with only a change in video card then that is where the problem is at.
I had mounted the heatsink to my HTPC with bolts and no gaskets or washers when I first got it. A few months later when I had the machine down I took it apart and added in some o-rings to isolate the bolts from the motherboard to avoid them digging into the PCB. The computer works perfectly fine. It's hard to say for certain, but if you were careful with the assembly then it probably didn't do any damage. Some o-rings, nylon washers, or even pieces of paper/cardboard gaskets can be used to avoid damaging the PCB.
Are there any other symptoms going on? Does it power on for a few seconds and then power down? It's possible that the card was not functioning to begin with. If there isn't any physical damage to the PCB then I don't see how the bolts could have caused the problem.