Hi guys could do with a bit of help, see photo below.

A friend of family asked me to pop round and have a look at her cylinder as have not been getting any hot water for the past week and having to use immersion heater.
heating is fine but no hot water.
im guessing this is a tap stat fitted? Haven't really dealt with many systems of this type. I took the head off the trv and found the pin to be stuck a little, sprayed a bit of silicone spray and tapped the pin till it popped up again as you would with a normal trv.
fired the boiler up (ideal Mexico) and let it warm up for 30mins, found the flow going into the top coil and just after the tapstat was hot but on the connection to the return coil at the bottom was stone cold?
she hasn't got much money so was trying to try a few things out first, I left and told her to let it run for an hour and see if she gets hot water, phoned me a couple hours later saying the water is still cold out of taps and the overflow was pouring out?
thinking the tapstat needs to be replaced and possibly a blockage on the coil?
what are your thoughts chaps?
Every day a school day blah blah!

A friend of family asked me to pop round and have a look at her cylinder as have not been getting any hot water for the past week and having to use immersion heater.
heating is fine but no hot water.
im guessing this is a tap stat fitted? Haven't really dealt with many systems of this type. I took the head off the trv and found the pin to be stuck a little, sprayed a bit of silicone spray and tapped the pin till it popped up again as you would with a normal trv.
fired the boiler up (ideal Mexico) and let it warm up for 30mins, found the flow going into the top coil and just after the tapstat was hot but on the connection to the return coil at the bottom was stone cold?
she hasn't got much money so was trying to try a few things out first, I left and told her to let it run for an hour and see if she gets hot water, phoned me a couple hours later saying the water is still cold out of taps and the overflow was pouring out?
thinking the tapstat needs to be replaced and possibly a blockage on the coil?
what are your thoughts chaps?
Every day a school day blah blah!