Gateway LX6810 - Random Shutdowns

I'm working on a Gateway LX6810 for the fourth time in as many months. Although I've left it on for as much as 48 hours in my shop without any problems, the customer states it shuts down completely (not a BSOD) at random - sometimes within a few minutes of startup.

Here's what I've done so far:

* Replaced the power supply with a Cooler Master 450w PSU (more about this later).
* Replaced the HDD (the old one showed consistent errors in CHKDSK). I've checked the new drive multiple times with both CHKDSK and Advanced System Care - no problems found.
* Disabled drive shutdown/sleep/hibernate in Windows 7 Pro 64-bit power options.
* Run MEMTEST - no issues found.
* Fresh Windows install + MSE anti virus - no virus/malware issues.

The computer is not being used for gaming - just Internet access and MS-Office.

I'm wondering if something on the motherboard is causing this. When the PC was brought in the first time, it was shutting off constantly. The "old" power supply was an almost new higher-end 500w unit that someone had done a very bad job cutting and splicing connectors on which may have caused a short.

Is there anything I'm missing? Could this intermittent problem be a motherboard issue?

Thanks in advance for any help you can provide.