If it's only the icons then your screen is fine. It's probably a software glitch.
If there are two sticks of RAM that will help troubleshoot:
a) Turn OFF
b) Remove one stick
c) Turn ON
d) look for errors
There's very little you can check yourself. It sounds like an error you should be bringing your laptop back for.
Quick check to eliminate software:
Get any copy of a bootable Linux. Ubuntu LIVE is the easiest. Boot from the DVD to Ubuntu and just look around. No errors? It's likely Windows which would need a reinstallation.
I think there's a strong chance of faulty graphics hardware though.