Starter not working on my 1988 Kawasaki Ninja

Hi, so I just got my 1988 kawasaki Ninja 750R back from the shop where they: replaced front and rear tires, Fork seals and oil, Front and rear brake pads, repacked muffler, Cleaned carbs installed new needles, Replaced sparkplugs, air filter assy and battery.
So I got it back drove it 50 miles back to the city I live in, and parked it overnight. The next day I had a little trouble with the starter (It made a loud cranking noise a couple of times then started). I drove it to work, it sat for 4 hours, and when I tried to start it, it just makes the loud cranking sound until the battery eventually starts draining.

I've been told that something is not catching?.

If it matters, it did sit out in a heavy rain for a few hours.

Wondering if anyone new more about this and how much it might cost to be fixed.
Thanks