Hi there!
Based on the serial number, the boat was built in 1980, but I don't believe you can tell the model from that number. Fortunately, it's pretty easy to tell the difference visually. First of all, Hobie only had 3 models of cats in 1980:
Hobie 14:
14' 3" Length over all
No trapeze wires by default, but could be added on
"banana shaped," asymmetrical hulls (V shaped bottom)
trampoline raised up on 4 pylons
No forward (jib) sail by default, but could be added on
Fixed mast (doesn't rotate), no diamond wires or spreaders
Mainsail will likely have a number 14 in a circle near the "flying H" (Hobie symbol) at the top
Hobie 16:
16' 7" Length over all
trapeze wires are default
"banana shaped," asymmetrical hulls (V shaped bottom)
trampoline raised up on 4 pylons
Jib traveler cars on forward crossbar
Fixed mast (doesn't rotate), no diamond wires or spreaders
Mainsail will likely have a number 16 in a circle near the "flying H" (Hobie symbol) at the top
Hobie 18:
18' length over all
symmetrical hulls (U shaped bottoms)
crossbars bolt directly to hulls, trampoline flush with hull
Hulls have "daggerboards" that slide down through the hulls through a slot in the hull
Hulls have deck ports just aft of the forward crossbar
Rotating mast with diamond wires and spreaders
roller furling jib that overlaps the mainsail/mast - jib blocks along inside edge of hulls/alongside trampoline
"loose footed" mainsail doesn't slide into a boom track
Mainsail will likely have a number 18 in a circle near the "flying H" (Hobie symbol) at the top
One piece of advice, before you get too far into fixing up the boat: check for soft spots. Given that the boat was left in the elements, it's possible that it wasn't well cared for and could have developed them over time. Press down hard on the decks and sides of the hulls. If there's minimal deflection, they're good. If there's significant deflection, or you hear a crunching or cracking, the boat has a soft spot. If there are only a few, they're easily fixed. If it's most of the deck/side, the boat is beyond saving. Check the length of the decks and sides. They're most common on the decks just forward or aft of the crossbars, where the crew frequently step or sit.
Hopefully the hulls are still in good shape and you can get it back out on the water again! Hobie cats are just about the most fun you can have on the water!
Post back with any further questions!