How do I get the codes? Have it towed to shop?
If you have an OBD2 reader, you may well be able to get the codes at home.
But if your car is not showing any warning lights, it might not have got as far as generating any codes.
Rumbly noise? Surely you know the sound of the starter motor? Might well be a fan (air-con, electronic, or main cooling).
Now you have the roof up (but not the small windows) you will still need to keep it under cover; as you say, after a short while, it might dry out, but actually, under the carpets, there is polystyrene insulation (acoustic and thermal) so the wiring will not dry out without lifting the carpets on each side. (I had similar when the front scuttle drains were blocked, and came in through the fresh air vent. I had to lift the carpets and mop up the water around the electrics, as well as mopping all the water I could from the carpet.)
Don't try the starter any more until you've got it much drier; electrics hates wet, and suffers if powered when wet, which is why you can save a phone by removing the battery immediately, and dry it out before putting power back into it.