You won't find a serial number on these. Heuer was particularly poor at keeping records and logging things, so whilst some of the more expensive models received serial numbers the divers didn't.
Only when Monnin first started making the 844 for Heuer did they get a serial number, and that was Monnin's serial number rather than Heuer's.
There's not so much to find out other than probably you already have.
The movement appears to be the ESA movement so is one of the earlier pieces, but then the dial is marked 1000 so will be towards the back end of that timeline.
Stick a new crystal on it and it should look almost like new as the bezel, dial and hands look in good condition. New crystal is about £10 or so. If you're in the UK I can highly recommend someone to service the movement and replace the crystal.