Since you've taken your dash apart, you can probably handle this. What you (or the shop) should check is whether the heater core is all full of crud which prevents hot water from flowing through. Also the water valve on the heater hose might be crudded up too.

It might be as simple as the inside of a heater hose collapsing & blocking the flow. If so you'll want to replace most or all of your hoses. You don't want that to happen to one of the big radiator hoses.

Depending on how bad it is, you can use something like Prestone SuperFlush or maybe you'll have to replace the heater core or the valve. If the heater core is that bad, then your radiator & engine might be the same way??