I have a 1991 Civic that is having trouble starting. I've checked everything electrical on it (distributor, plugs, etc) and it all checks out working. A few days ago, I managed to get it started by pushing open the "butterfly valve" inside air intake chamber.

I'm not real savvy about cars (probably obvious), but what controls this valve? The throttle cable is working and I thought that would be the mechanism that controlled this valve. Seems that's not the case. Any idea on what needs to be replaced?

The Intake Air System (Throttle Body) comprises several parts:
1. Throttle body
2. Throttle valve (butterfly valve)
3. Throttle linkage and cable (on one side of the throttle valve)
4. Throttle Position (TP) Sensor (on the other side of the throttle valve)
5. Fast Idle Thermo Valve
6. Idle adjusting screw

The throttle linkage and cable controls the throttle valve.

You may want to check your ECM for any codes being thrown. A problem in the Idle Air Control (IAC) Valve circuit should show up as a DTC 14. The IAC Valve changes the amount of air bypassing the throttle body in response to a current signal from the ECM, in order to maintain the proper idle speed.

I would counsel you to first perform many of the tests on the ignition system, in sections A and B, in the link below:

https://www.askmehelpdesk.com/cars-trucks/faq-how-troubleshoot-repair-maintain-honda-civics-46563.html

You need to be very careful working in this area, if you are not familiar with it--small changes can affect performance in a major way. 90% of starting problems are electrical-related, not fuel or air. So thoroughly check out the electrical first.