Insulate the walls, garage door, and seal the floor, there's probably no moisture barrier under the concrete slab.

There are waterproofing sealers for concrete available at places like Home Depot that you just paint on, and they work pretty good.

I'm doing the same thing right now, I'm installing a mini-split AC in my garage today so I can get some games out of my kitchen. I need to insulate the ceiling, redo the door weather stripping and and bottom seal, insulate the door itself, and seal my floor too. I'm not at all handy with houses, but that seems to be the extent of what most people do.

I'm mainly trying to prevent high humidity and fast temperature changes which seem to be the problem (although an equal number of posts claim to keep their machines in humid outbuidings for 15 years without issue). Most people see to keep their garage arcades around 50-55%, what was your dehumidifier doing?

They do work..But, I was told not to use on floors, walls only. He told me some people have put them on the concrete floor and they up heaved. So you may want to look into this more.

I sealed a garage floor with it 25 years ago and it has had no problems

Something to think about after you have it nice and dry. No fluorescent lights and a good solar film on the windows. Both the Sun and fluorescents will both fade your machines.
Good luck on your project. I dry walled insulated and climate controlled my garage for the same reason now with the snow and cold in Michigan, I want my garage back.

Open the walls up and spray foam.

The spray foam guys will make a 1" hole in the bottom and top of each stud bay - and fill each with expanding foam. Then they take a picture with a thermal camera to show 100% fillage.

The floor itself can be epoxied, just like a commercial garage.

What amazes me is the amount of snow you still have. I live in Central Canada and we've been snow free probably close to a month. Still snowing the odd cold day in the last couple weeks but just amounts to a little slush and it's gone a day later. No wonder you have moisture issues.

Back on topic... when this is all gone... you need to re-landscape your yard to ensure at least the 6-10ft next to the house is sloped away. That at least keeps the moisture coming down the hill off the concrete foundation directly. However, if enough is left standing, it'll find it's way there. Invest in a small submersible pump. One that you can hook a garden hose to.

My old house used to slope down big time. I put raised flower beds along the house to keep it's distance. I graveled the flower beds for drainage and trying to keep them reasonably clear of snow all winter. Then when the water pooled 10 feet away in spring I used my submersible pump once or twice a day to pump the standing water out to the alley. Within about two weeks the snow is gone and the water is too. Make sure you put a screen over the bottom of the pump to prevent crap getting sucked in and wrecking the pump. 3 pumps later I figured that out. I just used a piece of screen from a screen door to keep the gravel out.

Good luck on your issue. I will be following this thread as I have a similar issue.

What about the epoxy/resin recoating the concrete?

From my limited knowledge most moister problems can be solved with french drains, slope, and proper gutter spouts moving water away from foundation.

When i built my house the builder recomended after they tar the outer basement walls he put up a wavy type plastic that holds the dirt/clay in my area off the walls so the water could run straight down the walls to the drain tile below the floor for the sump pump. Works really good but it always sound like someone is taking a pee in my sump pump well.

Yes to all that and shrubs to soak up what's left over.

With that AND what's coming off the roof in back i can see why you have a problem. A French drain and gutters are needed on the ENTIRE back side of the house. Do you have gutters on any part of the back of the house?

Put cars in garage, pins in a guest room/game room.

Problem solved. AND no dirty hands trenching.