my little sister has a 90 crx and it has been doing this wierd thing where sometimes it will not start my dad has repalced the cap, rotor, plug wires, plugs, coil, fuel filter. It still seems to have the same issue. here is the wrinkle it starts everytime with the fuel cap off.

I am at a loss but it seems to be a fuel issue. mebe FPR or fuel pump relay?

 

starting issues like not wanting to start when you turn the key?

 

If the engine doesn't even want to crank, then it is possible you have a main relay issue(which also controls the fuel pump). It's notorious on crx/civics of similar years, and is solved by either soldering it or replacing it with a new one.