Hardware looks plenty good for Ubuntu so that shouldn't be a problem
Does your mobo have a built in gpu? If so, can you try running Ubuntu on that and disconnect the 5600 just to rule out driver problems. Although your boot messages didn't hint on any gpu driver problems.
The boot printout you had before mostly has hdd stuff on it. Can you post your partition scheme copied from a "real" partition manager? The windows partition manager you posted before didn't have the complete info on partitions (eg it didn't have the filesystem type for your linux partition). You can probably grab a copy of your partition scheme using the Ubuntu livecd.
Another thing to look at is, also in the grub boot editor, try leaving the "quiet" keyword and just replacing "splash" with "text". I've read before that the quiet keyword suppresses/shows different messages. If the messages you get is entirely different than the ones you posted before, post them here too.
Another thing to check is if the OS files were copied correctly. Boot into your live cd, mount your hdd, and just browse through the contents and make sure the important looking folders have stuff in them.
Since I'm guessing this is your first install, you can also try repartitioning and reinstalling. It wouldn't hurt since you don't have data yet and it should only take about half an hour.
Finally when all else fails, try posting over at Ubuntu Forums. I bet you can find hundreds of experts there more knowledgeable than me 😀