Assuming no hardware issues: Make sure that you have the latest chipset drivers installed. This is something VERY often overlooked that can explain large performance differences between a fresh install of an OS with the same hardware as before, and an old install.
*Essentially your PCI-E controller / bus may be operating underspeed, choking your GPU and resulting in the poor performance that you're seeing right now. (the controller running at 1-2 lane mode instead of 8-16 can absolutely decimate performance)
If installing chipset drivers is something you've already attempted, if it did nothing to improve performance, and "if" that machine is Intel, try using the "-OVERALL" command line argument
Aka, "infinst_autol.exe -OVERALL"
Should you attempt the -overall argument, note that it's generally best to do this from safemode to minimize the chance of a lockup / something going wrong during the driver swap.
As a starting point, I'd recommend checking what speed your PCI-E bus is actually operating at under load (in FFXIV:ARR). Tools like GPU-Z can display this information.
http://www.techpowerup.com/gpuz/
Also, don't get dismayed if you see a low speed "on the desktop" before stressing your GPU. [Power-management can throttle back the bus rate] Check your motherboard manual to get an idea what the speed of the slot your Radeon 7870 should be running at ... though if you see 1x, 2x, 4x, that's the problem and why FFXIV is performing so poorly.
EDIT: Re-reading your post strengthens my belief that this is the cause even more, as you can pretty much count on the "tech-person" who reinstalled the OS not doing the above (they pretty much never do more than the video-drivers). So yeah .... definitely give motherboard chipset driver installation a try first and foremost.