I have an Asus K53E running Windows 7 and have been having the biggest headache with Microsoft updates for some time. I'm not computer savvy about what goes on behind the scenes on my machine -- I just want to use it, keep it safe, and carry on. I admit I have been a bit of an ostrich about the update issue.

The past weekend, I have probably spent 8 hours in trying to work out the problem.

I am not asking you to work out the problem, because I have decided, since the machine is 4 years old already, to do one of two things:
1) buy a new machine (whether Windows 7 or Windows 8, or -- gulp -- Mac, is a different question)
or
2) factory re-set the current machine and SEE if that clears up the update issue and lets me have a do-over.

It seems to me that buying a new computer will RELY on my moving all my desired programs and documents over ANYWAY through a back-up I can make on a terabyte external drive, so not sure buying a new computer or restoring my old one is any more trouble than the other.

Buying a new one will a) cost me a lot of time to research the one I want, b) tap into a virtually empty wallet, but keeping the old one, just restoring it, means I c) have a nice case and a new battery for my current laptop. I like its keyboard. I know its interface. I have some software for it like Office that I can install on it again.

So, what are your opinions? That's still a fairly modern and relevant laptop you have there, I wouldn't advise replacing it for what sounds essentially like a software issue.  If you're set on not tracking down the issue and restoring anyway, I would go ahead and do that - if you've had it a little while then you'd benefit from a factory reset anyway, and you've already noted about backing up FILES and reinstalling programs etc so it sounds like you know what you need to do in that respect.
I would recommend taking an image backup of your machine before you reset it, just in case you miss some files or anything while you're backing up - you can do this with the free edition of Macrium Reflect found here - http://www.macrium.com/reflectfree.aspx
This gives you a full disk backup which you can restore if anything goes wrong.  Save it to your external drive and keep it safe, just in case.What sort of problem are you having with updates. Do you get an error? What EXACTLY is happening? Did you try running the Action Center?Keep in mind also if you resort to a factory restore you are back to square 1 RE: updates and would be starting over...I have had major problems in the past with updating windows 8, I found factory reset and correct installation works, I can maybe help you if you want.
Note: are you factory resetting from disk or harddrive because sometimes(though rarely) viruses and data corruption can cause damage to the hidden restore partition.