Would like help identifying Omega watch

I bought this at an auction last weekend to be cleaned up and get running for my boyfriend. It cost me $5. I had heard of Omega watches,but never knew much about them. So....I replaced the battery (there wasn't one, but after some research here, I found out which I needed and put one it. It still did not work. I had read somewhere that there was something to push after changing the battery but couldn't find it. Then, I found the little manual that came with it. I read the part on how to adjust the time and day and tried that. The crown (as I've seen it called here) came off when I tried to pull it out to the 3rd position. So now, that needs repaired. I also learned from this forum it has a scew-on back. I don't have a pic of the coil,but it looks to be in pretty condition.Here are some pics I thought to be the most important in identifying it. There's an inscription on the that says the watch was given to someone for 20 yrs of service. Thanks to any and all who are willing to help figure his out.

Hi,
it looks like an 196.0037 to me, Cal. 1310.
The price you paid is fair because without a running movement this sort of gold plated watch is only worth an equivalent of the useful parts as hands or the dial. If you really like to wear it try to look for a working 1310 and have it swapped. Often the problem is not only the coil but also the step motor. As far as I know parts for the movement are not available from Omega anymore. Also the bracelet is not original. I would date the watch to the early 70ies.

I hope that the info was helpful to you,

kind regards Max

Well, since he bought me a $1200 ring (1/2 off, so paid $600) for Christmas, I'd like to at least try to get this fixed. The battery I put in it says it an AG12, which I've found is equivalent to the 386, but it's also a cheap one. Maybe a better battery would help. And, I will keep my eye out for a running 1310, and maybe go that route. Thanks for the info and advice. Maybe, due to Christmas coming, I make out an IOU to give him under the tree.