Can a bad distributor affect the start of a vehicle? Car is: Honda Accord 1999?

I even have a check engine light
P1381
P1457? What does it mean?

Yes a bad distributor can cause a car not to start but the codes you have are the cause of your problem especially the P1381

P1381 which is Cylinder Position Sensor Intermittent Interruption
possible causes:
Faulty Cylinder Position Sensor
Cylinder Position Sensor harness is open or shorted
Cylinder Position Sensor circuit poor electrical connection

P1457 is Evaporative Emissions Control System Leakage possible causes:
Missing Fuel cap
Incorrect fuel filler cap used
Fuel filler cap remains open or fails to close
Foreign matter caught in fuel filler cap
EVAP purge control solenoid
EVAP canister
Fuel tank pressure sensor

After all the problems with this car, why are you still attempting to fix it?