I'd install a range hood from Ikea. They have different options. Here's what I would consider for your kitchen.

http://www.ikea.com/us/en/catalog/products/90339134/

will i need to do anything to the surrounding cabinets to make it look right?

Can you remove the little fence trim? That would help. Otherwise its not so bad.

Take off the little fence and paint it the same colour as the cupboards. Are you changing the hardware too? Something a bit less "colonial" would be nice. I really like the range hood, other than the fence but. There are lots of pictures on Houzz which will illustrate.

the part that really gets me is that it doesn't go to the ceiling. is like they didn't even attempt to make it look functional.

lol I could lend you some troll dolls.

I don't think you need to do anything to the surrounding cabinets to make them look right. Check the width you have to deal with and verify it'll fit. The top of the vent is height adjustable so you might be able to match the height of the existing cabinets or put it all the way to the ceiling. The model I showed you would still allow Lego men. :)

You could put a pipe or box on top to the ceiling to look like it is.

It is a more country style and a similar wood hood plus vent is over $1000 at a home center store - more through a K and B. It's more that it is not your style than that it looks bad. It is in the same style as the country cabinets. It does not have to go to the ceiling to function. Does it vent out the back? They didn't usually do cabinets to the ceiling back when that kitchen was done. You can go vintage with your kitchen and it could be sweet, but I doubt that is what you like. (If you do, check my "my pics" idea book.)

You should probably look at new cabinets or at least into refacing since this whole kitchen is not your style.

this section of cabinet has a rotten section at the bottom. I was planning to take the whole section out and build a pantry, but then I'll have to find a place for the microwave.

this the rotten section. it'll be the topic of another post.

Yep mold from the ice maker leak. You can have that replaced. It won't show once the fridge is in. You need a finish carpenter. Hopefully the doors are fine.