So ... this comes down to a doozie of a task ... replacing a stereo for elderly parents with something that will perform the way they remember their 'made in the USA' stereo performed.
What will make this task difficult is finding a receiver that pulls in stations as clearly as their KLH compact did back in the day.
For a receiver, I would look at something like the
Yamaha R-S300 at $280. This is a receiver that people go with when they are replacing older equipment from 20 years ago. The tuner seems to get high praise. Depending on where they live, you will probably need to get a pair of rabbit ears or some other external antenna to pull in the stations strongly. Also, if you want to get them a better turntable at some point, this receiver will handle turntables with magnetic cartridges. I would guess that the replacement turntable you got for them uses a ceramic cartridge and would connect using the AUX inputs.
I would not bother with the KLH speakers only because the foam surrounding the driver units has probably rotted out and they will need re-foaming.
I would take a look at the
Pioneer BS41 speakers that Amazon has discounted for $110. Yes, you can spend a lot more, but these speakers have been so well reviewed and will keep you within your budget. If you want to go with something else, try something like the
PSB Alpha at $300.
Good luck and let us know how it goes.
Rich