option 1)
After booting into the GUI, connect a physical keyboard, and press Alt+F1, then issue the dmesg command; you will have to scroll through alot of random stuff, but what your looking for should be in there.
# dmesg | more
option 2)
If you have a working network interface, on the build platform:
cd to the out/host/linux-x86/bin directory:
$ cd ~/android-x86/out/host/linux-x86/bin
kill the previous connection (if any):
$ ./adb kill-server
connect adb to your android device:
$ ./adb connect 192.168.0.123 (replace with the ip of your android device; can be viewed with the netcfg command from the android device)
view the log.. usually VERY long, and un-informative.. exit with ctrl+c
$ ./adb logcat
if the logcat doesn't have what you need, run a remote shell to your android device, and view the dmesg
$ ./adb shell
# dmesg | more
V/r,
Mike