My laptop occasionally loses internet, doesn't shut down properly...?

[Syrhid Westland]

Sometimes on my ASUS laptop, I experience a problem of unknown origin, which always seems to illustrate these symptoms...

1) Internet stops working
I'm unable to access the internet, even though the icon in the bottom left corner indicates it to be the same as before it stops working (My laptop uses Wifi btw). And speaking of which...
2) The icons for internet strength and sound control don't work
If I hover my mouse over the two icons, or click on them, they don't show anything or do anything.
3) The laptop won't shut down properly
When I try to shut it down properly, it stays idle on the "shutting down" screen, and would stay like that for more than an hour, until I just hold down the power button.

I don't recall this happening before early November, when I got my laptop back after my hard drive stopped working, forcing me to replace it. Since then, in the few weeks following, this event happens without warning, with no evidence as to what causes it. Then nothing happened for most of December until in the final few days when it started happening again. I've tried looking back to see what those two periods of time have have in common, but I'm at a loss. Has anyone seen anything like this before, and if so, how can I combat this?
P.S. I've had my laptop since the end of 2011.