ZX Spectrum +2 has a 6-pin DIN power connector with 3 different voltage levels, which makes it not compatible with most of the power supplies.
spectrumforeveryone.com has a very good guide how to use Cisco 34-0874-01 router power supply with ZX Spectrum +2 or +3. I could easily get this PSU for around $20 and change the plug to fit my machine. I noticed that it was enough to connect just one black ground cable (they are connected together inside the PSU). My PSU was also missing the blue wire where I cut the cable, only after opening the case I noticed the wire was there at the other end, so it was possible to make the switch as the guide advises.
On my keyboard keys 1 to 5 did not work at all. Extracting the keyboard from the case was easy, after opening it the prints on the contact foil led to a common connector on one of the tape connector’s pins. Next to these connector there was a diode with broken one of its pins (looked like it broke from the rust around it). I managed to solder it back to the circuit board, after which the keyboard started working normally.
As explained on this page, +2A model is very different to +2 and is basically a ZX Spectrum +3 with a tape recorder instead of FDD. The key external difference is totally different RGB video connector wiring, despite using the same connector (8-pin DIN):
The other difference is that ZX Spectrum +2A RGB port does not have a composite video signal.
How to tell that you have +2A or +2? Look at the startup menu – if you have “+3 BASIC” option there, you have a ZX Spectrum +2A.
Byte Delight has a beautiful document on Video fixes and video cables for all 128K models.
The old memory chips are frequently failing and need replacement. They are marked as AMS X 4, but they are regular 64Kx4 DRAM modules and a working replacement is for example NEC D41464C-15.
Z80 chips for replacement are pretty easy to get nowadays. Here are mine, that I ordered from www.littlediode.com once I broke the CPU by incorrectly plugging a module into the extension port.