I've had similar issues with two Phillips monitors, it's a hardware problem in the Monitors interface card, one would "Flip" on every few seconds, nothing fixed it until I put a new monitor on , then problem vanished. The other Monitor (Same brand), would take about 20minutes to warm up before the flickering behaviour stopped.
Try swapping the monitor outputs and if the problem persists then I'd say the monitor has a faulty interface card.
As for the lock ups it's very hard to say, if the Taskmanager is reporting very low or zero CPU use, then I'd be guessing the Network drivers are at fault.
I've had this with a couple of Dell machines recently, one laptop and two desktops, the only way I could fix them was to use the PowerShell scripts PSWindowsUpdate.zip which I downloaded from Microsoft (I am using windows 10, but it should still work on windows 7 if you are lucky), the scripts found a whole bunch of drivers which fixed the reboot / power / network issues on all the machines, although it has started happening again on one of the laptops.
I've also found that the Dell implementation of the Intel Rapid Storage drivers is faulty at a hardware level, and was corrupting the HDD of both the Dell laptops, I ended up changing them both to AHCI (You need to enable AHCI in windows before rebooting otherwise windows will not find the kernel driver at startup and will never start again so beware, check this link for a rundown on how to do this ...
https://winaero.com/blog/switch-from-ide-to-achi-after-installing-windows-7-or-windows-8/)
So try swapping the monitors, use the PSWindowsUpdate.zip to check for updates (It uses the same microsoft website, so I have no idea why the standard update doesn't find them and if you are using a dell with the Intel Rapid Storage enabled, you may want to consider swapping to AHCI, but the last is something you need to approach with caution as it may kill your machine if you get it wrong, switching back to Intel Rapid Storage in BIOS may not help after you have enabled the AHCI, I don't know why, but I'd guess windows kernel drivers get confused after automated repair)
Good Luck Jim ;-)