2-3 minutes is a long time for IE to start up. If you have a relatively new computer, ie, 2-3 years old at most, this is totally unacceptable.
The easiest solution is to reformat the computer and reinstall the operating system. It is likely you have some kind of malware or spy-ware that is taking up system resources, and this should get rid of majority of the stuff. To try and diagonose and remove them is far too involved and usually the easiest solution is to reinstall windows (takes about an hour) and start over. But this will mean you will lose *everything* on your computer, so backup any key filed or data before you do so.
If formating is not an option, you can try a few tweeks that might help things speed up.
First off, change your homepage to something that is simpler, ie, www.google.com loads up quicker than www.yahoo.com as its smaller.
You can disable the indexing service in windows. This service creates a database of all the files on your system whenever your computer is idle. It can take up allot of resources. To disable it, go to the Control Panel and click Add/Remove Programs. Click the Add/Remove Window Components. Simply unclick the Indexing services and click next.
If you are still experincing problems you can do the tweeks suggested at the attached link.
Disclaimer
Most of these process are a bit invloved, if you dont feel confident with doing any of these, then dont. And if you do start, ensure you *backup* all your important irreplaceable stuff (your work, pictures, movies, music etc) before you even begin - just incase you foul things up.