Reference designs for those 7770 rate the cards themselves at up to 150 or 170 watts, depending on configuration. They require 75W supply just from the 6-pin PCI-E plug from the power supply--that is in addition to what gets drawn off the motherboard. AMD actually recommends at least a 500W PSU for a single card, 600W for crossfire--and those are certified PSU's, not a generic one like it appears the OP has at the moment.
http://www.amd.com/us/products/deskt...on-7770.aspx#3
500W (or greater) power supply with one 75W 6-pin PCI Express power connector recommended7
600W power supply (or greater) with two 75W 6-pin PCI Express power connectors recommended for AMD CrossFire™ technology.

NOTE: Minimum recommended system power supply wattage is based on the specific graphics card and the typical power requirements of other system components. Your system may require more or less power. OEM and other pre-assembled PCs may have different power requirements.

Certified power supplies are recommended. Refer to http://ati.amd.com/certifiedPSU for a list of Certified products
Note the distinction there for certified PSU's. Generic ones have been known to have a nasty slope-off in efficiency beyond a 50-60% load. At 75% they can start to heat up a lot, throwing unwanted heat into the case as well as seeing their capacity slope off very dramatically. This extra heat can further compound cooling issues if the layout is already marginal on the cooling side.

Note also the 95W CPU--so potentially, the OP could be consuming about 40% or more of that PSU's expected reliable capacity on just two devices (95W for the CPU plus 150-170 for the card). That isn't accounting for drives, fans, memory, USB or other devices drawing power off the motherboard--nor the motherboard itself.

So, even if this can be tracked down to being a cooling issue... it may still be prudent to replace that PSU with at least a 600W certified one. If anticipating overclocking or upgrading CPU or GPU in the near future to something more powerful, I'd consider a little higher if in the budget since these certified ones tend to last a long time (or at least have a decent warranty time).