No remote/pull chains, how do I turn off fan without turning off the lights on combo unit
Check the wiring of the fan (after taking the regular safety precaution of turning off the breaker and double checking that the wires aren't hot), chances are that there are 3 connections (besides ground): neutral, lamp and fan. It's very likely that lamp and fan are jumpered together.

To disable the fan entirely you can then simply remove the jumper and connect the switched live to only the lamp.

To fix it properly you can remove the jumper and connect a separate switched live wire from the second switch to the fan. If that isn't in place you will need to run that extra wire which can be difficult depending on access from above.