Real upgrades are a coin toss. If everything on the previous system are compatible with Win 7 the upgrads will probably work normally. If some driver causes a problem, it might stop the install or lead to problems later.
If you want to try to save your current system, check the laptop's manufacturer and see if any Win 7 drivers are available for at least your Network Adapter. I like to also upgrade the chipset drivers first, but hard to say if it migh be necessary.
If you can't get internet access, use another computer. Many times, older anti-virus or spyware or firewall software can block access. Win 7 is very good about internet connection troubleshooting. Open The Network and Sharing Center and see if it shows any red Xes that might indicate a problem. Going to the Internet forum could allow for some folks more familar with this type of problem to offer help.
If you do a custom install, it will redo your registry and load new drivers. The old files will be left on your system, which you can delete if you do not need them by using the Disk Cleanup in the Accessories-System tools folder.
Another way, and I do not know for sure you would be able to activate even though some say you can, is to use the disk options button and format the drive prior to installing.