windows 7 - Laptop sometimes powers off during sleep; trouble diagnosing

I am trying to diagnose some issues with a friend's Lenovo IdeaPad U350 (3-4 years old), running Windows 7 Pro 64-bit:

1. Laptop turns itself off sometimes shortly after sleeping.
2. Generally running slow.
3. Wifi slow to reconnect.

Issue 1 started a few months ago and has been getting progressively worse; maybe once every 1-2 days.

Initially I thought all 3 were connected. However, there is a bunch of malware on the machine and I am now pretty sure that it is responsible for issues 2 and 3, but I am not sure if 1 is connected. Since we're having trouble cleaning all of the malware we're just going to wipe the drive and reinstall Windows, but this hasn't been done yet.

I am assuming issue 1 is not related to the malware and am trying to find the cause. That's the main subject of this question.

There were never any error messages or interesting items in the event log until today, when, upon restarting after a sleep shutdown, the "recovered from error" dialog came up citing a BSOD with BCCode 116, which by all accounts is display-related.

Things we've tried so far (all prior to the 116 error code):

• It's probably not a heat issue. This was my first thought. Friend reports possible excessive heat but we're not sure, and it is summer. Fan is running normally. We cleaned the fan and air filters as well. Temperature monitoring does not show unusually high temperatures. Also it never happens during periods of activity. We also tried leaving it in front of an air conditioner, and leaving it on freezer ice-packs when not in use with no effect (and ice packs still somewhat cold after problem occurred).
• It's not a battery issue. Battery appears to be in good condition, is not generating excessive heat, and is running at about 90% of its design capacity.
• It's not a RAM issue. At least, full memory diagnostics passed 100%.
• It's not a hard drive issue. SMART reports nothing out of the ordinary; SpinRite read-scan has no issues. Drive is < 12 months old, and appears to be in excellent condition. No unexpected filesystem error aside from occasional minor errors presumably due to power loss.
• I reseated hard drive connector, keyboard connector, RAM, wifi, and battery (everything I could easily access) just in case; no change.
• It's probably not a driver issue. All Windows updates, hardware drivers, and latest BIOS updates installed. (Q: Could it be possible that a broken update / malware is causing an issue? Shutdowns on sleep don't seem to be a malware symptom, but could be a driver issue.)
• It does not seem to be a Windows installation issue; sfc /scannow reports all files passed.
• It is related to either sleep mode or display power off. I do not actually know. I do know that it never happens during normal activity. The pattern is always when my friend walks away from the machine for awhile, and it goes to sleep, it sometimes is no longer on (and not in hibernation) on wake up.
• As for issue 3 (wifi); the slow reconnect is relatively new. It does not appear to be a router issue; nobody else connecting to that router has observed any issues, and the issue seems to occur in other locations.
• Thinking issue 3 was perhaps related to issue 1, I ordered a replacement wifi radio thinking perhaps the hardware was failing. It has not arrived yet. I will be replacing and observing, however...
• ... today's error message seemed to be a missing piece suggesting a display related issue.

Based on the error message, I'm leaning strongly towards a display problem. My friend reports no unusual display glitches. I have my doubts that it is a driver issue, mostly based on having faith in Intel's integrated graphics drivers, and also the randomness of it is a little strange and smells of hardware problems.

So my current theory, based on the above, is a failing video controller or LCD driver, with the sluggishness and wifi problems being unrelated to that and caused by malware. Does this seem like a reasonable theory? Are there any other good possible explanations given the above? Is there a possible connection between issue 1 and 2/3?

If it were my own laptop I'd be satisfied to keep buying replacement parts and trying them until something worked, but for this we want to finish quickly with little wasted time and money. If it's a display hardware problem then the only real options at this point are to live with it until if fails completely and eventually buy a new laptop. The machine is past warranty. But if it could be a different problem it would be nice to fix it and move on.

I feel like I keep running into dead ends.

Current strategy, I'm thinking, will be:

• Replace wifi radio (might as well, since we already ordered it)
• Wipe drive and reinstall windows
• Ensure all drivers are up to date
• Continue to observe

But that's not really a concrete solution. If I can come to a more solid conclusion, we can take the right action immediately.