USB Drives not working

I have a strange issue with a couple of USB drives, they are both the same Seagate model and are self powered not USB powered. When I plug either of them into my desktop no matter what USB port (Front/Back or USB 2.0/3.0) it takes a while but comes up to be usable, then when I try to access them or leave them it become unresponsive to browse or do anything and then drops off with the error message USB drive not recognized.

I have plugged them into a separate laptop and they work perfectly fine and if I plug a memory stick into my desktop that works perfectly fine as well, just these 2 drives seem to have an issue with my machine. I also notice a strange issue when plugging in a drive, when the USB port of the cable touches one of the USB ports on my desktop the screen cuts out for a second and then comes back on, but once I get it plugged in the screen is fine. I am running Windows 8.1.

Could this be some power related issue causing this?
Any advice or ideas welcome please, I am hoping but doubt it is to do with Windows.

The first thing I do with similar issues is shut the computer down and unplug the power cord from it and any drives. Then after about 30 seconds I start up and try again. I get it most frequently with messages about it would work better with USB 2.0 ports. And Yes, you could be having a problem with the power circuits between the power supply and the motherboard, hard to find and fix without replacing parts. Static electricity can also cause such a problem with the screen blanking out, see it on my workbench once in awhile.

Good advice but just tried the unplug solution and not working, I think you are right that this is probably being caused by my powersupply to my board and there is something going on with that.