MSR63,
The reason your laptop boots so slowly off the network is it's trying to connect to mapped drives.
As cdogg suggested, try using a local user account without any domain credentials or mapped drives. It'll boot much faster.
As a test, if you have another computer available on your domain, try this:
1) Disconnect all mapped drives on the laptop (maybe do a print screen of each, or put the paths in a text file so you have them for later)
2) Start both computers.
3) On the laptop, map a drive to the second drive. Make sure you can open a folder and view files on the share.
4) Now shutdown both computers. Leave the second computer off, turn the laptop back on. Does it boot slowly?
5) After the laptop boots, turn on the second computer.
6) Shut down and restart the laptop. Notice any boot time differences?
The slowdown comes because a comoputer is trying to re-connect to drivrs that are mapped. If your not connected to your domain, or the drive is from a pc that isn't powered on, for example, then the booting pc will take time until it reaches a timeout period. This is why you should log onto the laptop locally when you don't/can't log into your work domain.