94 ranger
The P0556 is for a fuel pump relay primary cicuit fault.
Not sure why it runs better when the CEL is on, but may have to do with the computer reverting to the programmed in "Limp Home" mode, so it's running off pre-programmed data, rather than corrupt PID inputs from a faulty sensor, or circuit.
Look to the underhood power distibution box fuel pump power relay, they are a common problem part & it's plug in connections for corrosion, bent pins, spread sockets, or a problem with the relays B+ feed wire from the computer, that tells the relay to close it's contacts to feed power to run the fuel pump.
On the MAF sensor, with a DVM, back probe check the MAF sensor electrcal connecor for B+ voltage at KOEO.
If thats ok, check between the Signal & Signal Return pins for output voltage to the computer. At idle it'll be low, like 0.2-1.5 volts, at increased rpm it should rise to like 2.0 volts.
If not, look to a dirty, or faulty MAF sensor, or wiring, or corroded or damaged connector pins, sockets or wiring.
If it's dirty, pull the MAF sensor, let it cool & spray clean it with a plastc safe, non residual cleaner, like CRC MAF sensor spray cleaner. DON'T touch the sensor & keep it squeeky clean when reinstalling.
THEN, look up stream to find out Why it got dirty, as it should only see clean filterd air!!!!
Some trouble shooting thoughts to get you started, let us know how it goes.








