I had a new laptop I was setting up for someone that bluescreened immediately on connecting to Wi-Fi.
At first, I suspected bad hardware, as the driver was correct, & I checked other settings. It ONLY bluescreened when you connect.
But I found out that if you go to Device Manager, then open properties for your Wi-Fi under Network Adapters, you can go to the advanced tab & change the connection type.
I found that by setting it for the most basic 802.11 option, it would then connect without bluescreening. If anyone else has this problem, then maybe this will help them fix wi-fi bluescreens.
That's the most common type of connection I believe and found in most router settings, and usually with a combined setting to use either 802.11b and 802.11g.
If the machine is setup to do minidumps you can get it to bluescreen and then using 'Who Crashed' or 'Blue Screen View' you will be able to see what caused it.
Also there may already be a clue in the Windows Event Viewer.
If it is a new laptop it probably will connect using Wireless N (which is backwards compatible anyway)
What is make and model of laptop?
A thread here with posters having the same problem with various workarounds.
I had my system BSOD when it had too many connections, OR connecting to some of the newer routers in wi-fi hotspots. I updated my driver and now it's rock solid. Fantastic.
My driver was w22n51.sys (2004 vintage) for an intel 2200BG card in my old laptop. Basically, the old driver was not aware of the new modes and channel switching capabilities of the newer (2010-2011) routers.
Oh, it wasn't rebooting due to redirects or anything. I checked that. It also did it with brand new/clean installs, so it wasn't malware. It did it with 2 separate brand new laptops with Windows 7 64 bit, as well as brand new windows 7 32 bit setup on the 64 bit machine, so it definitely was not Windows itself.