AC Acting Up!

I found a new unit I'm thinking about replacing it. The reviews say it is easy, plug and play, quiter, lighter, and one said takes a half hour. Anybody done a replacement? I don't know if it will fit the existing hole. How can I know for sure? This is it, $718...
https://www.rvpartscountry.com/dometic-13500-top-unit-only-a-c.html

Update for my continuing saga: Dometic has a toll free number. They cross referenced the capacitor part number and gave me the updated new number. All the places I looked were out of stock. Except Ebay. And they were the cheapest. Will get it in less than a week. Camping world wanted twice the money, and maybe I would get it in 2 months, maybe not. South Carolina's heat and humidity won't wait for that. The ac is blowing cold air, it just takes assistance to get the fan going. The ac only has two capacitors. I replaced the "start" capacitor thinking that would do it. Not starting, right? Wrong. Then I watched a video about house ac's. I'm getting an education. House and RV ac's are similar. He started the fan by hand. Then showed how to discharge the other capaciter, called the "run" or "duel" capaciter and replace it. It's the one with 3 prongs, one is compressor, one is fan, the other "common". Apparently, these have a tendency to go bad. DO NOT do this your self unless you know what you're doing, a capacitor that is not discharged can hold a lethal zap. It started right up. I'm not saying it's going to fix mine, we'll see. Stay tuned.

After watching numerous videos, I'm still baffled about AC's. I'm still trying to get some helpful clarification. Maybe I'm not being clear, or making this harder than it should be. I turn the ac on from the thermostat. There is a humming. I'm guessing this is the compressor but maybe somebody knows and can tell me. Then, I kick-start the fan with my hand by reaching up and giving the squirrelcage a spin counter-clockwise. It starts running and blowing cold air. It cools the camper down. Then it starts blowing cooler air more slowly, makes an increasingly louder noise and cuts off. Then as it starts to warm up, I repeat this. I have seen on Youtube this is likely a bad start capacitor. The AC has two capacitors. I replaced the smaller black one I'm told is the start capacitor. It says start capacitor right on it. But it's acting the same. The fan is not starting. I've ordered the other capacitor I'm calling the run capacitor, or 3-pronged duel capacitor, and will have it replaced next week. It has three prongs, and two are labeled fan and compressor. I'm hoping that will fix the problem. Maybe the two capacitors work together, and the three prong duel capacitor is responsible for helping starting AND running. But I'm just guessing. I don't have a clue. That's why I'm here, to see if anybody does have a clue. Guess that's why AC techs get the big bucks. Or maybe they don't know either, and are just winging it. Again, has anybody ever confronted this problem? If so, PLEASE dispel the mystery. Summer is knocking on the door!

Another update...So far it seems to be working as it should. Maybe cleaning it and replacing the two capacitors did the trick. Will know more when the brutal South Carolina summer comes. We just had 97 and it's not even here yet. Thanks for hanging with me everybody...

Also glad you got it running.