In my Corolla the engine was not cranking from.

Rewrite symptoms and information in reply.

PO102: Mass Air Flow (MAF) Circuit Low Input

What does that mean?Basically this means that there is a problem with the Mass Air Flow (MAF) sensor or circuit. A more technical description would be that the MAF circuit had lower than expected voltage (air flow). Other MAF sensor circuit DTC trouble codes are P0100, P0101, P0103, and P0104.

SymptomsYou will likely not notice any serious drivability problems, although there may be symptoms such as a general decrease in power or sluggishness.

CausesA code P0102 may mean that one or more of the following has happened:

The MAF may be disconnected, or a wiring connection may be bad
The MAF may be dirty or otherwise contaminated (Note: if you use a reusable oiled air filter, be careful not to apply too much oil or that can contaminate the MAF).
The MAF sensor may be faulty
The vehicle computer may be faulty (very rare)
Possible SolutionsThe simplest thing to do is to reset the code and see if it comes back. Then start with the cheapest, easiest repair procedures:

Verify that the Mass Air Flow Sensor wiring is connected properly and that there are no broken / frayed wires.
Inspect for any air leaks near the MAF sensor.
Take the MAF out and clean it using a spray cleaner such as brake cleaner or electrical contact cleaner. Be gentle with the sensor.
Check the voltage of the MAF sensor (refer to a repair manual for vehicle specific information)
Replace the MAF sensor.

P0113:Intake Air Temperature Circuit High Input

What does that mean?

The powertrain control module (PCM) monitors the temperature of the air entering the engine. The PCM supplies a 5 volt reference voltage to the Intake Air Temperature (IAT) sensor. The IAT is a thermistor that varies resistance based on temperature. As the temperature increases, resistance decreases. Low temperature results in a high signal voltage. When the PCM sees a signal voltage higher than 5 volts, it sets this P0113 check engine light code.

Potential Symptoms

There will likely be no symptoms other than illumination of the Malfunction Indicator Lamp (MIL - Check Engine Light / Service Engine Soon).

Causes

A code P0113 may mean that one or more of the following has happened:
†Internally failed IAT sensor
†Faulty connection at IAT sensor
†Open in IAT ground circuit or signal circuit
†Short to voltage in IAT signal circuit or reference circuit
†IAT harness and/or wiring routed too close to high-voltage wiring (e.G. Alternator, spark plug cables, etc.)
†Faulty PCM (less likely but not impossible)

Possible Solutions

First, if you have access to a scan tool, is there an IAT reading? If the IAT reading is logical then the problem is likely intermittent. If the reading is less than -30 degrees, unplug the connector. Install a jumper wire between the harness connector signal and ground circuits. The IAT temperature reading on the scan tool should be maxed out at the high end. For example it should be 280 degrees Farenheit or higher. If it is, the wiring is okay, and it may have been the connection. If it isn't install the jumper wire between the IAT signal circuit and the chassis ground.

If now the IAT reading on the scan tool is maxed out then check for an open in the IAT ground circuit. If you get no reading at all on the scan tool, it's likely that the sensor signal is open or the 5 volt reference is missing. Check using a DVOM (digital volt ohm meter) for a 5 volt reference. If it's there, then unplug the connector at the PCM and check for continuity on the IAT signal circuit between the PCM connector and the IAT connector.

These codes will not effect starter itself if it is a problem. The small wire is the voltage from key that makes starter operate. Did you test starter itself? Is it an automatic? Try to start while in neutral?