I'm by no means an expert, I'm more theory than reality at the moment, just learning.
Honestly a lot of the time you can't really know exactly what the cause is, till you start fixing it by, pretty much, starting to rip things out till you find the problem. I mean without looking it could be anything from a completely incorrectly done base, to a blocked drain meaning when it rains rather than actually draining, its just gradually soaking everything.
The thing to do is call a few builders, have them take a look and give you a quote, which shouldn't cost you anything. Now, a crap builder will tell you its almost nothing but say maybe put a new dpm down, another level of concrete, then whatever.
A good builder would hopefully make some educated guesses as to whats wrong, hopefully giving you an idea of whats wrong, how to fix it and how much it would cost but give you an idea how expensive it could get if something else was wrong. You shouldn't be under any obligation though and in the long run the money might be worth it.
At the end of the day its up to you to work out if you can afford to fix it but, damp tends to lead to mould, slowly or very quickly so its worth fixing.
A fixed, fully working garage conversion(with permits, can't remember if this is a "proper" job or not or just a guy living in a garage) will add value to a house rather than a leaky, mouldy garage making people question if there are problems elsewhere, so you can view it as an investment?