Repeated BSOD error 0x0000001e, even after factory reset

UPDATE: Here's where I am:

- I wiped the hd with DBAN. Did a clean install of Win7.
- Ran MBAR, got the all clear.
- Installed Wi-Fi driver; downloaded both MSE and MBAM, which provided clear scans, as well.
- TDSS Killer also provided a clear scan.
- I've been following the tutorial on doing a clean OEM install, in terms of slowly adding things back.
- I added Adobe and Java products, per the suggestion.
- Installed and ran CCleaner.
- Manually installed two missing drivers via Dell & Intel: USB 3.0 and the SM Bus Controller.
- Currently have two unknown devices in Device Management. Google tells me they are a Free Fall Sensor & Fingerprint Scanner. Do I need to install these, or should I wait?
- Installed Speccy. Temps are in 40s/50s. I can post a screencap if you guys want?
- So far, no new BSOD yet.
- The folks in the thread I linked above are currently helping me with my external hard drive which I have the files backed up on. Apparently, it's infected. So, as of right now, I have not been able to return the backed up files to the laptop.

Britton,, I've finished adding back the files. It's been a few days going and still no BSOD. I've been monitoring the temps, which seem stable. The laptop goes home today. I explained to the owner the best I could about what to watch out for and what all I did. If she doesn't experience any problems in the next few days, I'll come back and mark the thread as solved.

Will keep you guys updated!

Update: Checked in with the computer owner. They've had no BSOD issues! Hooray! Thank you all again! Will happily mark this thread as "Solved."