Will Hybrid Car Work Without Battery. The high-voltage HV battery is used to start the engine. From what Ive read the Civic Hybrid has a separate starter so it doesnt need the hybrid battery to start up.

The truth is you cant. On electric motor propulsion alone a hybrid vehicle can usually travel a short distance of around 25 miles or so. In certain hybrid vehicles you can drive without the battery however it is not recommended as it can cause permanent damage to the hybrid system.
The engine is started by motor-generators MGs operating on the HV battery not a conventional starter motor operating on 12V auxiliary battery.
The other major concern with hybrid car reliability is the hybrid battery. As a result your car will no longer be able to drive. Your Hybrid Accord would set a check engine light as well as an IMA light if the hybrid battery died. Personally I think both are to blame.
