The first thing I'd be checking is if the battery has been removed!
If it hasn't then snip it off as soon as you can. Those things leak even more than the capacitors do!
Speaking of the capacitors, it is definitely a must to replace all of the electrolytics on both the motherboard and the CPU card. They cause a Lot of havoc with these machines!
As for the keyboard, yes you can find ps2 to amiga adapters on ebay, lyra is one of them.
For getting a display from the machine you have a few options. The cheapest would be to build a gbs8200 + gbs control (or get one premade from
http://microbeetechnology.com.au/) with an amiga rgb cable.
A decent option is also an ossc with Amiga rgb scart cable. Both of these upscalers can be used on other retro computers and consoles so they're good options.
If you want to go all out, get a zz9000. It will give your workbench modern 1080p screen modes through hdmi, and has pass through for all other screen modes, as well as usb, Ethernet and up to 256meg ram.
Welcome to the rabbit hole!!