After some more research, I think these are Toro Flo-Pro valves:

PDF of valve

And you can replace just the solenoid which is what is broken on mine (I think, I'll update later if this proves to be correct):

Picure of solenoid with wires

Can anyone confirm?

Barcino,
Yes you have ID'ed the valve correctly as being the dreaded Toro Flo Pro with the quick link (or quick fail) solenoid. The good news is that Toro stopped making the Flo Pro a number of years ago. The bad news is, as I have been told, that they will continue to supply parts for the valve for only another few years, then it will go the way of the dinosaur. Then your only option will be to cut out and replace the entire valve for a faulty solenoid or diaphram. Toro sold MILLIONS of these valves which they obviously knew was a poor product, then sold them by the millions, and then leaves contractors such as myself to deal with the aftermath by not supplying parts to repair them.
BTW, if you are able to find parts for your Flo Pro, the new solenoid will not be the quick link solenoid, it will have leads coming off the solenoid like all the other well designed valves.

All Wet
Texas Licensed Irrigator #1897 since 1984

If you contact Toro Irrigation customer service they can supply replacement diaphrams. The diaphram is easy to replace (unscrew the ring). With a replacement diaphragm your valve should work. While you're at it replace the solenoid and plunger. This much easier than cutting the valve out and replacing with another valve.

While you are at the supply house, asked for some sealed wire nuts, and replace those butt splices.

Barcino, everyone gave good advice - All Wet's was the best. It's not fun or easy to replace valves, but definitely worth it in the long run.

Hunter and Rainbird both make great 1-inch valves that will bring years of reliable operation. Stay away from Weathermatic "Nitros" - they still have problems with their solenoids.