It wasn't so hot that I could not hold my hand on it and the clicking is coming from the white plastic piece mounted on the compressor
Similar, without undoing it it appears that there is one wire going in at the top and 2 at the bottom and is clicking about every minute. When I place my hand on the compressor it feels like it is slightly humming.
You need to replace those parts at the side of the compressor. They pull straight off there is nothing holding them on other than the tight fit. Sometimes you need a screwdriver to help work them off. I put an image below with them removed so you could see they are straight pins that hold them on. Be sure the power cord is unplugged.When you go to get these parts the best thing to do is call around to some local appliance repair shops, ask them if they install compressors. If they do that will be the place to go. I do not expect you will get them for free but I can tell you that every time I install a compressor there are always extra of these parts in the box. I have a lot of them laying around and I would expect you would get the best price from someone who does that work. Those parts are the overload and start relay, the clicking is the overload. I know power is present at the overload because it is clicking and most always when a compressor is bad it will be burning hot or room temperature so I think those are bad.If you found my answer satisfactory please login if you are not already logged in and please leave an ok or better rating. If you have any questions use the reply to expert link.Thanks,Barry