Are you against building it yourself? I wholeheartedly recommend it. You can keep the same budget, too.
For reference, here's a desktop that I built for myself just 1 year ago...
viewtopic.php?f=49&t=52782That hardware bundle was about $1,200 from NewEgg at the time, but will obviously be cheaper now. Newer generations of the CPU and mobo exist (3000 series CPU and x570 motherboard) but I stuck with the previous generation because it was "tried and true." You would need to add a graphics card and optical drive (if desired) or you could reuse these items from your current desktop if possible to keep cost down (GPU could always be upgraded later). The case that I got is huge, you would probably want a mid size tower instead and that would also be cheaper, or reuse the one you have now if possible. You could also save money by getting a 1TB HDD instead of the 4TB that I got. Cheaper SSD exists too, but Samsung EVO is king. So yeah, totally doable for $1,000 and you'll have a better PC because of it. I doubt the PC from that link has an 80+ Platinum PSU in it.
My Sale Thread -
7% off all marked prices!! SNES and N64 added! I am selling around three quarters of my video game collection as well as some other odds and ends!
I want to buy
Universal Game Cases, if you have any spares please PM me! I'm looking to only deal with members that have good BST feedback on this forum.