I don't think the safe-mode issue you're having is related directly to the graphics card. You could be having a graphics driver issue. In which case, you need to boot in safe mode, remove whatever previous graphics drivers yoyu may have had installed and install the latest stable driver for your card.
You also have a PSU issue. You should not be running that graphics card with a 200W PSU (I don't know who told you otherwise, but they were mistaken). It may run temporarily, but it will stress the PSU beyond its intended operating range and it will cause problems.
Before purchasing any equipment, be sure to do the due dilligence of a quick Google search for compatability or minimum requirements. In this situation, doing so, would have yielded multiple results, all indicating a PSU requirement of much greater then 200W. In fact the 2nd link takes you to the Radeon HD 7770 information page. Upon arriving there, you are presented with a link to the "System Requiements" section. (Link below) This will tell you that there is a minimum requirement of a 500W PSU, with 600W recommended.
I hope this helps.
Motherboard: Asus M5A97LE R2 | CPU: AMD PileDriver FX-6300 Black Ed. @4.1GHz | Cooling: CoolerMaster Hyper212+ | RAM: 8GB G.Skill RipJaws DDR3 @1600MHz | GPU: XFX Radeon HD 7850 DD | Display: Asus VH242H | PSU: OCZ GameXStream 850W | OS: Dual-Boot Windows 7 Pro X64 / Linux Mint MATE 12.04 X64