First problem first. It sounds like the mechanical power switch has either some arcing, or oxide build-up, on the switch contacts causing intermittent or full contact closure. The replacement part is most likely NLA (no longer available).

Without knowing if you have any electronics experience, I'll first give you the simplest thing to try. Unplug the unit and then give the switch switch about a dozen or more rapid on/off pushes - it'll sometimes burnishes and cleans the contacts.

Plug in and test to see if that eliminated the problem.

If not, it time to take the cover off - only if you do have some electronics experience! Unplugged of course, use a small jumper lead with alligator clips on both ends and locate the power switch on the inside front left corner. You'll see two wire wrapped posts coming from the switch - jumper them with the clip lead, plug in and test again.

If that worked, and sounds OK, you can try the first cleaning method I described but try to spray some "lubricated contact cleaner" into the internal switch area - depending upon switch construction, you may or may not be able to. Some switches Sony used at that time were gray plastic with a small wafer board crimped on to them which contained the contacts and you could get a little cleaner in there.

If that can't be done, or didn't work, I'd simply have somebody solder a jumper across the power switch to bypass it. It's really not creating a safety hazard (maybe put a sticker on the back and say "power switch bypassed" to inform somebody else taking the cover off) and basically is just the same as leaving it on all the time. But I would plug it into a power strip with a switch to really turn it off when not in use as it's probably drawing about 20 watts all the time.

By the way, if the jumper didn't work, I wouldn't pursue it any further.

The remote on/off problem now, if you really do have electronics experience, may be caused by the 3.6 volt backup battery, soldered in, on the main circuit board near the display - it's the same one used on many older PCs, and are still available.

Of course, if you like the smell of new cars and electronic equipment... it may be time to go shopping!

Without going the "home theater" route, stereo receivers are also still an option and would consolidate your current separate tuner/amplifier setup into a single product.