Rep Power: 0

I recently obtained a 2005 Civic VP 2 door coupe. Changed the ignition switch/lock assembly; the one that came with the car was for a 2001-2002 Civic and could be turned with a screwdriver (no key needed). After an unsuccessful trip to locksmith for key programming (scan tool would not communicate with car), I had a shop diagnose and repair a broken wire at the fuse box, a melted wire at the main relay, and replace a bad main relay. They were able to program the new keys.......sort of.

The car will recognize the keys and start every other start attempt. (LITERALLY)

After a successful engine start, the green key light will flash constantly as soon as the key is removed. At this point when the key is inserted, the car will crank but not start.
After the key is removed again, the green key light goes out. Insert the key once more and the green key light comes on for 2 seconds, and the car will start.

I have repeated this over and over just to verify what I'm seeing. Has anyone experienced this before?
What should be my next move here? Thanks in advance for any and all help.