2004 Sentra hard to start, engine code multiple cylinder failures

This code is for the throttle position sensor.
https://www.autozone.com/engine-management/throttle-position-sensor-tps/nissandatsun/sentra/2004

engine problem

I would check engine compression, fuel pressure, catlicit converter as it might be blocked. Is the transmission/gearbox OK?

the p0505 is a idle code look at the p0301 that is cylinder one misfire check the spark plugs and wires

Please try to replace fuel filter and clean the fuel the tank then try to check the fuel pump and the strainer of the pump

check the RPM booster switch which boosts up the RPM of car when AC is switched on.

please have a test performed to confirm the integrity of your head gasket. this era of these cars were prone to failure, causing coolant to leak into the cylinder thus a misfire. it is typically most noticeable on a cold start, and can cause long cranking times, as well as a rough idle when first started. good luck!

I hate to be the barer of bad news, but may be the head gasket.

My car started with rough idle. Then very hard to start in cold weather. Next started overheating, but no output from heater. Trickling sound from behind dash board. Overflow bottle overflowing.......

I replaced the water pump, radiator cap, thermostat, coolant, fan belts, power flushed the system. Nothing worked. Some research gave me the answer.

The head gasket leak was allowing exhaust gases to enter the cooling system, displacing the coolant. After use, as engine cools, coolant is sucked back into the system and coolant seeps into the cylinder. This gets worse over time.

First thing you'll notice is the rough idle as the spark plug burns off the coolant in the cylinder. (This is especially true at low temperatures.) If it is the head gasket, the other symptoms will follow as time goes by.

we have the same problem...it is your fuel regulator.