Just bought a 86 Crx SI standard transmission that was running fine at the time except for a bad battery. I replaced the battery and the car worked fine for a couple of days. With the new battery I was able to start the car a couple of days but then one day I drove it to work. Started just fine no hesitation, able to drive it to lunch, but when I tried to drive home it wouldn't start. Didn't make a single noise. Dashboard lights, head lights, raido, ect all work perfectly. Was able to push start it. Luckily was on a ramp in a parking garage so just pushed it back enough to run it down the ramp and pop it into second. Ran fine, drove the entire way home with no problem. Which amounts to an hour commute in heavy traffic. Still won't start, only way to get it running is to push start. Jump start does not work

Things I have done and tested;

Replaced starter and ignition switch
Make sure there was good connections on the battery and starter for power and ignition
tested with a multimeter
**power is getting to the starter
**ignition switch is getting the "start" signal
**Voltage drop test was fine
**Battery is charged
Looked for blown fuses

Right now I'm a bit puzzled. Anyone have any ideas what it could be?