Rca f35755mb - when i push the power button on it clicks on then off three times and then stays off. what is going on?

Sounds like main board fault. Short circuited component/s at it. Contact any service technician; or the authorized service center. If you wish to get some details; check the site linked here. Surf the site with patience. Pull up older posts. http://electronicshelponline.blogspot.com/ . In most cases, the main board might have to be replaced. If so, a software [firmware] update too might be necessary.
These blinks [flashes] are fault indication (Error Codes). From the number of blinks occur at one time switch ON, you can get an idea about the faulty circuit section inside it. This will make repair easy. These are called blinking codes. Make sure about the exact number of blinking of the standby/power LED, by switching On & OFF the set, for at least two times. Count it carefully. If you wish to get some details, check the site linked here. It has details about blinking codes, and fault locating procedure, to many popular brand TVs and other devices.

Set-up (Programming) procedure is too much to type in here, and is not practical and it will differ brand-to-brand remote controls. If you wish to get more; check the site linked here. It has set-up code list & set-up procedure to many popular brand remote controls. See it in "Mosaic" or "Magazine" view. It will make surf easier.
http://electrohelponline.blogspot.com/

A number of possible reasons for this---failing part in set or even bad connections on main board in the set----model listed is prone to going dead with high pitched squeel etc.

Replace the three Capacitors CP150, CP120 and CP114 very common problem for that model You can get that RCA repair kit from www.tvrepairworld.com RCA and GE are the same TV.

Push and hold power button. If it cycles and blinks on/off in 3s or 9 times, it is a power problem. Replace the deflection board. Cost about 250.00

click here you would find the details for led codes. you may select any laptop. codes remain the same.

replace the flyback which is the 270125 flyback. You can get the 270125 Flyback repair kit at the following link which contains the flyback plus detailed instructions on CD
http://www.tvrepairworld.com/

I had the same problem and it was the cp150. It cost me $2. Easy to change. I would look in the back and see if any of the capacitors are popped or bulging out on the top.

Here's th link to RCA codes.
http://remotefinder.rca.com/default.aspx?site=rca

I have the same problem; I push the power button green light comes on tv clicks but doesn't come on.