Glad to be of help, Tami.
As to your questions and comments (not in the order posted):
Great to hear you've got a freebie line on the MS stuff through your college/university, that helps save a lot of money as I'm sure you've noticed.
As to system requirements of Win8 over Win7, required specs are actually about the same. I have a feeling given your described usage habits that you'll likely prefer Win7, though. Pretty much any system with 2GB of RAM or more and manufactured in the past five-plus years should be plenty. All those Optiplex 755's are Intel C2D machines (dual core) and should be plenty.
As for data security on the failing drive, you've got two options:
1) If it's still operational enough, yank it out, put it in a better machine after disconnecting the other hard drives, and run
DBAN on the turkey. A single 0 (zero) pass will be plenty.
2) If it's too far gone to reliably get a wipe done, take a screwdriver set to the thing and tear it apart until you get to the platters (how? just keep removing screws over and under labels until it starts to come apart), then just run the strong neodymium magnet inside the actuator across the platter surfaces and scratch 'em a bit, that'll sufficiently damage the thing enough to not be worth the money to try and rebuild and recover for even the deepest pocketed crackhead. If you're curious to learn a little something while doing that,
watch this video.
Given the additional problems you've just pointed out, it sounds like my suspicions are right on. Those bulging caps are likely directly related to the hardware problems you've had with the machine leading up to this point.
As to the cost of machinery versus durability and usage length... I'd be surprised if you got another six-eight years out of a $200 refurb like the Optiplex 755. The thing to remember is that they're already about 2-4 years old already. Figure your functional usage time-span to be around another 2-4 year range with the thing with some proper care. Considering those Optiplexes were over a grand new, and they're well designed and reviewed, it won't be an unreasonable expectation. Quality electronics cost money to get the usage span you got, but if you can pick up a quality used machine for far less than 1/4th the price of the thing new while still having 1/3 to 1/2 of the life expectancy ahead of you... you see why I (and others) recommend business/enterprise grade refurbs now. It keeps perfectly good machines out of the trash heap to be properly used until failure point, and reduces overall needless supply/demand for new crap. And for the money, that's about the same life expectancy or better than I'd expect out of new consumer-grade at the same price point.
To my brief earlier point, though, it's hard finding quality builds anymore under at least half a grand new or factory refurbished. Most of this stuff is designed to be disposable krep to continue driving sales, even getting into the lower end enterprise sector these days. Software requirements and hardware advancements are no longer sufficient to actually drive growth and sales anymore, so manufacturers design the things to fail to keep sales up at the price of environmental impact and your wallet. In this context, now you know why Apple seals their batteries inside their laptops and phones and wraps their phones in glass... and nearly
everyone uses cheap CapXon capacitors in their electronics.
If you do buy a refurbished desktop like one of the Optiplex 755's linked, keep in mind they're third party refurbished. Sometimes they're great, sometimes something will slip through. You're already ahead of the curve now. Order with confidence knowing what to look for with the machine once you receive it to take full advantage of the short warranty they have. Look for bad capacitors on the mobo and through the vents on the power supply and while the case is open and you've got yourself well grounded to a chunk of metal make sure connectors and cards are well seated, and use
UltimateBootCD to do some basic hardware tests after you get it. Run Memtest86+ for about 6-8 hours to make sure no errors pop up, and run the drive manufacturer's extended drive diagnostics on the hard drive. If anything bad shows up during the tests, send it back for an exchange immediately to avoid longer-term issues... otherwise, you're good to go.
Any other questions you want to ask me specifically, you know where to find me. :)