Though WiFi is supposedly to a standard, I have experienced several occasions where one particular adaptor simply refuses to connect reliably to a router /access point. Even worse I've had the experience of getting it to work (eventually) to fail again next time the PC switched on.
Odd things I've come across that can go wrong
1) Adaptor will connect using WEP, but not WPA (typically sees signal but will not acquire IP address)
2) Makers describe security strings in different ways (e.g. 'number of bits' in WEP van be specified in 2 different ways)
3) Different drivers required depending upon exact age of adaptor (have to check serial number)
4) Adaptor will work with manufacturers software, but not with Windows 'wireless zero' (I've also seen this the other way around).
If an adaptor doesn't work within a few minutes, it is likely you'll spend hours and even then not get it working - try a different make/model.