I am actually wondering if I have a very similar unit to you. I have a silverstone case which takes a mATX board its quite a nice looking black case, maybe about RU high. And i have a dual core Pentium G620 in there with 4GB ram. Its an Asrock board with a B3 chipset. The case takes 1/2 height cards. I was looking at getting a GTX750ti for it. I am currently running the onboard graphics and its working pretty sweet. I dont have the same problem as you do.
I was wondering if you take the ATI card out and then use the onboard graphics, does it still have trouble waking from sleep mode?
What case do you have? I have Silverstone lc17 and the r9 270 fits easily.
Yes the CPU graphics (apu?) Worked fine. It's only when I installed the GPU did I encounter issues.