Trouble Code 35 indicates a problem with the Idle Speed Control (ISC) circuit. It will be set when the closed throttle engine speed is 200 RPM above or below the desired (commanded) idle speed for 50 seconds. Possible causes include:
1) Vacuum Leak (High Idle) - Also check for binding of throttle blade or linkage.
2) System too lean (High Air/Fuel Ratio) - The idle speed may be too high or too low. Check for low regulated fuel pressure, water in the fuel, or a restricted injector.
3) System too rich (Low Air/Fuel Ratio) - The idle speed will be too low. May exhibit black smoke in exhaust. Check for high fuel pressure, leaking or sticking injector.
4) Foreign material in throttle body.
5) Faulty IAC Valve electrical connections.
6) Faulty PCV valve.
7) Faulty IAC.
8) Faulty ECM.
Trouble Code 44 indicates that the O2 sensor is showing a persistently high exhaust oxygen content (lean), despite the efforts of the ECM to increase injector on-time (thus increasing fuel delivered). Integrator and BLM numbers may indicate > 128 by a substantial margin. Code 44 is set when:
- O2 sensor voltage remains below .2 volt for 60 or more seconds
- System is operating in "Closed Loop."
- No Code 33 or Code 34
Possible causes include:
1) O2 sensor defective or lead shorted
2) Lean injectors (dirty or blocked)
3) Water in fuel
4) Exhaust leaks upstream of O2 sensor
5) Fuel pressure too low
Now you have both codes, that leads me to believe you have a lean running condition. This is most probably one of 3 things which are easy for you to check. First check all the vacuum hoses coming from the intake manifold for cracks or a loose connection and the intake manifold for leaks. The IM can be checked with a can of starter fluid sprayed around the base to see if you get a surge in idle. Next pull the hose off the fuel pressure regulator. If there is gas in the hose, you have a bad FPR which is easy and cheap to fix. Lastly, check fuel pressure at the rail with a cheap gauge you can buy at any auto parts store. With the key set to "on" and the engine on, you should have 55-61 psi for that engine. If not you have a bad fuel pump or a clogged fuel filter. The one other thing could be the injectors but I would leave checking those for last.