First check if you can access those disks from My Computer. Don't use shortcuts, just find it and click. If it's not there or give an error message, either something is wrong with the disk or with the computer.
If it can be accessed: just make new shortcut (right click on an empty part of the desktop, choose New>Shortcut) and let it point to the drive letter currently assigned to your Seagate disk in My Computer. Or edit the current one to point to the right drive letter. Or realise you don't need those shortcuts if you know how to use My Computer and delete them.
The first thing to do if they can't be accessed: find another PC (friend, family, work, where-ever) and see if you can access them there.
If they can't be accessed elsewhere either, well, it's just a backup disk. So you won't lose any data by throwing it away and buying a replacement, will you?
If they can be accessed elsewhere but not on your PC, something is wrong with the PC. It can be hardware and it can be software. A PC Cleanup suite can certainly cause such things (why did your PC need cleanup and why did you trust such a program?). Anyway, you can't claim it didn't work: your PC is cleaner without those 2 disks.
It might be time then to find a repair shop and let them solve it. Take your recovery disks (or Windows disk and driver disk) with you, just in case they need it.
Best of luck,