Currently, I'm using old BCM43xx driver, that goes with kernel 2.6.22. Performance loss of using old firmware and legacy kernel driver goes fine with me.
Article I used to setup wi-fi is HARDWARE BCM43xx from Gentoo-wiki.
Firmware from current Windows XP driver is too new. It's of v4 family, while kernel driver officially supports only v3.
The most recent v3 firmware (from bcm43xx-fwcutter readme), that is freely available, is DELL's old driver - 184.108.40.206 ftp://ftp.us.dell.com/network/R102318.EXE. If you want, you may download only bcmwl5.sys from here, as there is no need in other files for bcm43xx-fwcutter.
Somehow, High Precision Event Timer (HPET), being Enabled at BIOS, weirdly hanged wpa_supplicant. Disable it and wpa_supplicant runs smoothly.
Also, turning off 'Wireless Hotkey' is recommended (but not needed).