I am not sure what you mean by reset your network or recognizing your router. Equally I do not know if you are wired or wireless or how they connect. I will assume it might be a mixture of both and your DHCP server is the router.
Given that, can you try a couple of things………
Start with 1 PC, open a command prompt and type “ipconfig”. Do you get an IP address? If not then that’s likely to be part of your issue. If you do then check the default gateway address, it should be the address of your router. Can you ping it? If you can move on and repeat this for all the PCs on your network. This ensures that you have connectivity between every PC and the router.
Next can you ping each other? By this I mean PC 1 can ping PC 2 etc….Be careful of firewalls on each PC, ping might be blocked and as such give you spurious results!! Assuming all that works…..
Then, can you all access the internet? If so then you network is fine and its likely to be file sharing configuration in Vista thats causing you grief.
I am being a little vague in this answer I know but all I think I can do is point you in the right direction,
If you need anymore help then either repost or add to this question.