I had a set of Logitech x530 on which the sub recently started doing something similar.... I replaced them with the Eris E3.5s which I'm loving so far, hopefully they don't go the same way!
Anyway, I had a brief look online and not clear what the manufacturer warranty term is, but it appears that it varies by where you bought them from, with some offering 3 years....Worth checking that first!
Otherwise, they could be repairable if you're confident with disassembly/soldering etc. but as it sounds like it's the power stage that's gone you'll need to be careful to not shock yourself.
I found one video where the issue was that the power switch had burnt out (although tbh if that was the issue I'd be more worried about them starting a fire!), they look pretty simple to take apart so I would imagine an easy fix:
https://www.youtube.com/watch?v=4uymOyxaVvE - I'm not convinced that is the issue in your case though, as they do eventually power up (albeit in a screechy way)
Other reddit etc. threads I found suggest anything from a blown fuse to a blown capacitor (which is fairly common on amps and similar items)
@Vince - Any other suggestions? (Sorry, I know everyone always tags you in anything to do with faulty electronics
)