Aside from the obvious question, "Why are you still using IE?"Have you tried to use another browser on your desktop?
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When is the last time you did a . . .
Defragmentation
Check Disk
Cleared out cache
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Have you tried to reboot in 'safe mode'? Does this work?
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Network Connectivity -- You say you're using your laptop. Are you connecting to internet the way you do on your desktop? (same network)
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If you can use another browser and/or doing routine maintenance does the trick, you can always then just reinstall IE. If not, then maybe it's time to run the . . .
Anti-Virus I'd recommend using Panda online or Avast if you can't get to your own.
Malware
HiJack This
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But it sounds to me as though you probably have one of those nasty trojan viruses.
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Final question . . .
Where's your backup?