i need to know if any of the threats can be a danger to my laptop because of the shared router.

Yes and no. It is important to remember that as far as the router is concerned, anything from the trusted side, that is, your network, is safe. So what that means is if your desktop is infested with malware, the router will see that malicious code as being from a computer on the trusted side, think it safe allowing it to infect your laptop. This is why it is essential that all computers on your side of the router also have a software based firewall, such as ZoneAlarm, Comodo, Online Armor, or even Windows Firewall. There are some corporate type routers that analyze all data passing through them, but most home users have pretty basic routers with NAT.

the router is connected to the desktop by an ethernet cable and i run my laptop from wireless so when i do reformat will my laptop still connect

Yes - independently sharing a single Internet connection is a major advantage to using a router (besides the added security benefits). But note in most cases, you do not need to reinstall broadband - you simply let your router assign any new (or new again) computer a new IP and it should just connect with no problems.

BTW, reformatting is ALWAYS a last ditch effort because when you format your boot drive, you lose all your hardware drivers (especially the newer ones needed for SP2); data including documents, photos, music and videos; email; favorites/bookmarks; downloaded programs and updates to them; custom configurations; and worst of all, you will end up months, or even years behind in critical security updates and patches.

I suggest you run through Cleaning Out Malware first to see if you can bring it back to full performance levels.