As noted, I dismissed salvage as a not-terribly-helpful strategy(if luck were with you nobody would have to suggest it; and if it isn’t you can wait a while. I was curious about the existing computer for two reasons:
If the RAM is compatible with one of the systems being discussed here that changes how much you need to get with the new system: 8gb is arguably the minimum worth targeting; but whether or not the RAM you have can be added changes whether or not it is worth considering the 4gb options or just skipping them.
HDD is of interest just because having your video recording on a different spindle from the OS/game install will make your life more pleasant.
Based on the constraints outlined; my main concern is trying to find the one that will feed the GPU properly, since the whole exercise will go poorly with only Intel HD Video to show for it:
The HP 6200 does not declare that its PCIe slot provides a nonstandard amount of power(with standard being 75w); but all the GPUs listed as HP option parts appear to be 25w or less models. Might just be because they were selling to conservative businesses that needed typing boxes; but might also indicate that bus power is limited. PSU is listed as 320w; but is proprietary; and appears to have no SATA, Molex, or PCIe connectors of its own; power for two HDDs is provided by ports on the motherboard. This obviously bodes ill for cards that require a PCIe power connector; and makes replacement more difficult.
The Dell 790 specifically states 35w on the MT-case configuration; the spec sheet also says it has a 265w PSU; but it is a normal ATX pinout.
The GT720 you have now should work in either(barring seriously janky firmware issues); it’s ~20w.
A GT1050 could be tricky: per Nvidia, it’s a 75w card with no supplementary power connector; so it won’t work unless the Dell is just being pessimistic; and is substantially more demanding than anything the HP claims to work with; but the HP never explicitly states a lower wattage.
However, there are some GT1050s (like this one) that do have a 6 pin PCIe connector; which might mean that they don’t lean on bus power as hard; though they don’t seem to specifically say. There are anecdotal reports of a GTX1050 working in one; but it certainly isn’t a formally supported configuration.
Unfortunately, anecdote is about all you’ll get for either one on GPU upgrades, since both only have vendor-spec cards from when they were released, which are a waste of time now with the improvements in GPU performance being rather more substantial than in other areas of the system.
My taste runs toward the Dell; PSU is standard which comes in handy if you need a replacement or upgrade to feed a punchier GPU. Case build quality will likely be incrementally better; but the difference is minor. It is, however, undeniably more expensive.
The HP is cheaper; and if it actually supports 75w bus-powered cards it is definitely the cheapest option I can find within the vendor constraints imposed; and spares aren’t currently hard to find or terribly expensive; though there are no upgrade options if the PSU or motherboard don’t cut it for the GPU you want; you’d be tossing everything but the CPU and RAM.
I’m not sure what else to say. If fate smiles on the HP it could work out quite handily; and for rather less. If not; it will be badly GPU bound until you toss both motherboard and PSU; which will promptly devour any savings. Unfortunately, I can only come up with a thin trickle of forum speculation in either direction; and have neither for testing myself.
