Network and keyboard light sttill on

Hello,
Since I 've purchased an Emachines T6420, more than 3 years, I had many problems with this one. The actual problem is that :
1/ whenever I turn off the computer, the light on the keyboard (numlock) is still on. I haven't had this problem with the others either old or new.
2/ This computer is wired internet ,connected to the router, and the light at the plug ( in the back) still also on, and I think that the network is not shut even when the computer is powered off, and may be this is the source for virus, malwareS... attack my computer . I had many time the malware and virus attacks and most recently just happened 3 days ago.

Could you help me .
Thanks