Ok...so, is this "new" adapter replacing an older one that stopped working, or are you switching from wired to wireless?
If you were replacing Wi-Fi adapters to take advantage of a speed increase (i.e. upgraded from Wireless-g to Wireless-N), then uninstall the new one & put the old one back on. No BSOD = problem with the new adapter and/or its driver.
If you're switching from wired to wireless, reconnect the Ethernet cable & uninstall the wireless. Again, no BSOD = problem is with the adapter and/or driver.
If neither option is availabe, test the adapter on another PC. If it causes BSOD on the other PC, the problem is the adapter and/or driver. If it doesn't, then a) your PC has an issue, or b) your PC doesn't want to play nice with the Wi-Fi adapter.