A pleasant "find"?

[dayid]

I live in a home that was built in the late 1960's. In our laundry room there were some mostly empty shoeboxes piled behind the water-heater. Most had cleaning products (rubber gloves, old vinegar, etc) in them, if anything at all. Cleaning them out today I happened upon an interesting looking blue box. Inside I found this. You can imagine by surprise and excitement. However, just from my knowledge (or complete lack thereof), it looks like the band (in the least) is a fairly-junky knock-off or replacement-band. The movement I can't really test on the watch, plan is to stop by a jeweler later this week when I have time off work and get them to take a look at it and (a) tell me if it's real (b) tell me what is broken and if it's going to be a fortune to fix.

Right now the winding mechanism is all the way out, and pressing it in does not keep it in - the minutes hand revolves loosely, so without cracking it open I can't really tell what type of a situation I have.

I've found images online of similar watches, but all of the similar day-date models have roman numerals for the hours, whereas this one has stones instead. I'm not sure if I'm just searching improperly or not, but this inconsistency with just this watch (as far as I know) makes me doubt it's authenticity. Likewise, from the FAQ on this site, the shape of the crown, as well as the ROLEX font-shape makes me curious.

The only other thing in the box was a 10-year warranty slip from "Accutime Service Dept 1001 Ave. of the Americas 6th FL New York, NY 10018". There is no owner name/information/serial filled out on this slip, but it makes me question authenticity as well.

Any information about this model (whether it is real or fake) as well as any suggestions on finding additional information about this would be greatly appreciated.

The only other Rolex I have ever even seen in real-life (AFAIK) is my father's Rolex that he received from his father, so I have little-to-no knowledge of them outside of the FAQ's I have read on this site so far tonight.