Ok, the win 8 Pc its brand new? maybe have some bootloader problems, security problems, or so. If you can boot ubuntu on it or another distro, you should be able to run chromium, check the Arch its build on(32,64,powerPC,etc), if the image you r using its 32 works on 64 arch, but not vise verse, so if still cant boot chromium, make sure that its just the GUI (the window system), by click on ctrl+alt+F2, if you see a terminal (some gray text in a black background), try to type "
sudo -su"(the pass should be facepunch, or chrome) and do a "
uname -a" this will show you some arch and system info. This is important, now we now that the linux basic shell (the chromium shell) its working and you have just GUI problems, this could be drivers, blacklisted modules, etc. but if it never boots, some kernel, system incompatibility, CPU Arch, basic start on its missing, or its not loaded. Then you should see on Windows 8 all the drivers, hardware, system info, like video card, audio card, touchpad, ethernet, wifi, etc, then check if chromium has support for some of them, maybe like i said, if you can boot Ubuntu LiveCD, Debian, Fedora, Mandrake, etc, it says that Linux has drivers and supports your hardware =D, you just need to port some of them.
Cheers. =D