There could be a couple of fundamental things going on. First of all, one of the connectors on the unit could have slight oxidation on it, in which case you can clean it with alcohol, and then use a fine emory cloth to lightly scrape the oxidation off.
Some units have a relay that delivers power to the unit, and those contacts can become oxidized and/or corroded, by humidity in the air. Sometimes you can tap them with a hammer, and they will make contact. Get a replacement, but in the meantime, your air will be on.
I'm going to refer you to some general googled sites, since there are many things that you can check yourself, and hopefully fix it: l
http://www.google.com/#sclient=psy&hl=en&source=hp&q=++air+conditioner+won%27t+turn+on&aq=f&aqi=g1g-msx1&aql=&oq=&pbx=1&bav=on.2,or.r_gc.r_pw.&fp=ab08b906c4821279
The following web page explains problems with Ancor A/C units, and also gives various companies that have taken over Amcor, since they have gone out of business, and hopefully it will be of help in case you need parts:
http://amcorairconditioner.com/
Good luck, and hope this helps.

Never try to repair or dismantle the air condition yourself. Incompetent repairs result in loss of warranty

and can endanger the user and the property.

Problem Cause Solution

The air conditioner does not function..........No power supply. Connect to a functioning outlet and switch on.

Is the LCD light flashing............... Empty the internal water container.

Timer function is active................. Deactivate TIMER function.

The air conditioner does not seem to perform...................In direct sunlight. Close curtains. Windows or doors open, many people or a heat source in the room.Close doors and windows.

Dirty filter.................. Clean or replace the filter(s).

Air inlet or air outlet blocked.................. Remove the blockage.

Room temperature lower than the selected value..............Change temperature selection.

The unit is noisy. Unit stands uneven................. Place on an even, solid surface (less vibrations).

The compressor does not work......The overheat protection is probably activated. Wait 3 minutes until the temperature has

decreased, then turn on the unit again.

The remote control does not function...............Distance too great. Make sure the remote control is correctly

Remote control signal not detected when aimed at the control panel..............The batteries are drained. Replace the batteries.

To correct problems that have not been described in the table and/or if the recommended solutions fail
to solve the problem, contact an authorized service center.

The above mentioned areas of trouble shooting are listed above, and diagnostic repairs will need some expertise and knowledge of the voltage supplied to the unit and circuits.