No hot water even if heating elements work (solar/boiler combination)
If the hot water is hooked up to your faucets, then hot water should eventually come out regardless of the re-circulation stuff. That is, unless the check valve is the wrong way or the pump isn't letting water flow. Then you would just get cold water.

EDIT
I see from your comment that the system was previously working and no work has been done. The check valve must be installed in the correct direction. I don't know your entire system, so, it's difficult to know what's wrong. It seems like there would need to be a check valve between the hot and cold line at last faucet in the plumbing run. Then water from the cold side wouldn't be allowed to come out the hot side in case of a restriction in the hot side.

EDIT 2
Thanks for the drawing. I thought you had a recirc pump so that hot water was always instantly available at the outlets. I think the check valve would be better placed on the output of the pump, but I don't think that's why it stopped working. Although I don't know the likelihood, the problem could be a failed check valve. I don't see how else you could get cold water bypassing the heaters after previously working.