Ugh, that sounds horrible. You don't have any control over the OS at all? If you do, you might want to uninstall whatever is related to Logitech, and then re-install the motherboard drivers (chipset, primarily, and USB if there are some). You might also want to do a System Restore to revert the machine back to before you first installed this keyboard, so that you can at least use the machine properly.
My mother uses this same keyboard and has never experienced an issue with it, certainly not like this.
Intel Core i7-3960X, GIGABYTE G1.Assassin 2, Kingston 16GB DDR3-2133, NVIDIA GeForce GTX 770 2GB
Kingston HyperX 3K 240GB SSD (OS, Apps), WD VR 1TB (Games), Corsair 1000HX, Corsair H70 Cooler
Corsair 800D, Dell 2408WFP 24", ASUS Xonar Essence STX, Gentoo (KDE 4.11. 3.12 Kernel)
"Take care to get what you like, or you will be forced to like what you get!" - H.P. Baxxter
<Toad772> I don't always drink alcohol, but when I do, I take it too far.