My car is a Very hard start and when it does start it idles well for about 20 seconds and then dies. Also when idling well if accelerator is depressed engine tries to stall, whn you let up it comes back to life. The check engine light tells me that codes 25 and 51 are present, which is the IAC valve or a vacuum leak (25) and a lean air/fuel ratio (51). I have checked the fuel system and replaced two cracked vacuum hoses, spark plugs, air filter…to no avail…anyone had this problem??
The Idle Air valve is a vacuum leak, although it’s a controlled one. 
A vacuum leak could be present in the dashboard, cruise control servo, brake booster, injector seals, etc. and the only real way to verify a vacuum leak is by connecting a vacuum gauge to the intake manifold and see what’s going on. It’s also the quickest way of knowing one way or the other.
“Lean” can happen from too little fuel, or too much air. A dirty fuel filter, or weak fuel pump, can result in too little fuel. Too much air can come from air leaks (vacuum leaks). A pcv valve, or it’s leaking hose, can be at fault. The vacuum hose to the brake power booster, or the booster itself, can be split or ruptured. It’s difficult to check a IAC valve without a scan tool to read the counts. You could try disconnecting the wire connector from the IAC valve and see if it makes any difference. I don’t know.
The 95 Neon is one of the few 1995 cars with OBD2 code readout. Why not take the vehicle by one of the parts stores that reads out codes for free (e.g. Autozone) and get the OBD2 codes read? They are different than the ignition key codes and may give you some additional information.
Quite frankly, I would go ahead and replace the IAC valve and hope for the best. If the computer is reporting an IAC problem, it makes perfect sense to go for that component without trying to complicate matters further. The part costs under $50 at auto parts stores.