Thermostat needs a C wire

In this photo, @speadie (a community member) has created a perfect description of my environment. I just want to confirm that if this diagram is executed that the basic needs of both heating and air conditioning will be met. If there are more advanced features that will be disabled (i.e. learning), I am ok with that. Just want to make sure my hvac will work. Currently with a 4 wire (Rh, W, Y ,G with Rh jumpered to Rc) only the AC works but not heating. With a standard thermostat, both work. I would remove the jumper between Rh and Rc if executing configuration in diagram. Any thoughts?

It’s weird that you say cooling works but heating doesn’t, as that diagram indicates that there is no contiguous path across Y and G, which would generally be required for cooling to work properly. Do you have photos of your setup?

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My ac system is from the early 90’s. No c wire. Thats why i went with the Nest model “e”. No c wire needed. It has a built in rechargeable battery. Works great, and has Alexa integration.

I apologize for the confusion…the diagram is what I think I WANT to do.
My current system is 4 wire
R wire to RH jumpered to RC
W wire to W (Heat)
Y wire to Y (AC)
G wire to G (Fan)

For some reason, if I put the R wire on RC I only get AC or R wire on RH only get Heat.
The obvious answer is that the jumper is defective.
Tried a second unit with the same result.

A simple solution was to try a $29 t-stat and it worked but no wifi controls.

can you please take a picture of your setup and post it here? i’d like to see the thermostat wires, and the furnace wires.