Desktop shortcuts won't slow your computer down.
Assuming you have Windows XP:
Start - run
Type
msconfig
in the box and click the 'startup' tab.
You need your firwall and antivirus to automatically load, but if you have Office, your printer, games, other programs that you really don't need to start up automatically, then remove the ticks. You can always change it back if you need to.
Then click 'apply' and 'okay'
You usually have to reboot.
If you are in any way nervous, you can use a free little program to help you
http://www.windowsstartup.com/startupinspector .php