1) as TB says, netbooks come with wireless built in, you don't need a dongle.
2) you say "the old modem" but you need a wireless router, not a modem.
You've also not mentioned anything about the netbook such as what make and model it is, what version of windows it's running (if it's even running windows).
So, ditch the dongle, make sure your "old modem" is in fact wireless capable (if it's not contact your ISP for a wireless router, they'll probably give you one for free) and then if you still can't figure it out after reading the docs that would have come with the netbook post soome more details about it.