Can somebody identify this Moentrol valve?
As far as I can tell, what you have looks correct. It's very similar to the 3570 and that would require a 1225 cartridge.

However, I see that Lowe's (and probably most hardware stores) sells kind of a one size fits all cartridge by Moen for their older valves. The 1200E is most likely what you need.

1200E - Metal faucet - "Replaces single handle cartridges installed prior to 1990"
http://www.lowes.com/pd_27473-866-1200E___?productId=4750863&amp;pl=1&amp;Ntt=moen+cartridge

1225 - Plastic faucet - "Fits all Moen 1 handle faucets (excluding Posi-Temp and ExactTemp)"
http://www.lowes.com/pd_27375-866-1225___?productId=3133585&amp;pl=1&amp;Ntt=moen+cartridge

If it doesn't fit, don't forget that you can always return it and try the other. My guess is the 1200E, but it's going to be one of these two.