Random reboots and IE issues

I'm having problems with IE not launching when I click the icon. A process is started for each attempt at launch, but no window. I have to go into task manager and shut down each iexplorer process, sometimes multiple ones, in order to get a window to come up and sometimes it takes several attempts to get a window. I've done all the malware scans and came up with nothing.
I'm also getting random reboots when exiting sleep mode. Not every time, just sometimes. could these two issues be related??

My laptop has started having the same problem with IE. A reboot seems to have fixed it. Could this be a memory problem??

 

I'm running Win XP pro SP2, IE 6.0, and 1 gig ram. I also downloaded a .NET update today. The browser seems to load ok, but i've only tried a couple of times so far. I'll know better in time.