It is many times seen that USB splitters are giving proper/full power. did you used any splitter or usb cable extension wire? even, one case usb port of on front of the cpu cabinet (of the computer) was not giving enough power but same time on-board usb ports worked fine.

Thank you sir,,,will try it and post the result asap....

You have to use Acro mode in transmitter , not Heli mode.
Better create a new model in transmitter with acro mode.

I want to give a brief summary of my doings and problems. Please suggest me what should be done next to make it work.
 Doings: 
1. Used Tx in factory settings except I have changed from Heli to Acro mode for Radio calibration.
Problem :
Radio Calibration still not happening.

2. Tried powering amp 2.6 via USB only by removing and putting again the JP1 jumper.
Problem : Still apm is not powered by USB only & it was never done earlier also.

3. Checked Rx Chnls using ESC. Rx is found to be OK.

4. Checked apm powering by connecting many USBs in different ports & in diff systems too. Not working at all.

5. Calibrated all params like compass, accel & also installed firmware by powering apm via Lipo & connecting to Mavlink.
Problem : When radio calibration is up there.....FAILURE !!!!!!

6. My Tx was in Acro mode....stick set mode 2....PPM...Rx CH 1-4 serially connected to apm CH1-4....
 WHAT SHOULD I DO NOW.......?

whats the status of red light in receiver when connected to apm?
also check

put the jumper jp1,

Connect only  rc input, USB and just one ESC

disconnecting all other cables(power module, gps,compass, ESCs etc...)

check the status now.

In the picture in your reply #6, the receiver LED doesen't seem to be on. Is that still the case?

If you have access to a multimeter power up the APM and check the voltage on any of the inputs '+' pins.

Yes sir,,I did that...disconnected all the modules(PM,Compass,GPS..) and only connected rc input and one ESC,,red led of Rx is solid and corresponding motor worked....what to do next ??

Now you need to complete the radio calibration.

NO its working fine sir...just tell me the proper connection of Rx to apm plz...I have connected CH1-4 of Rx to CH 1-4 of apm input serially and using PPM Acro mode in Tx for radio calibration and still problem persists...

Did your motor work while connected to the APM or directly?

Ya motor worked,,I have checked connecting the ESCs one by one also and corresponding motor worked,,,but they got only throttle values not others...plz tell me or give me some images of proper interfacing of channels and everything...cuz still im unable to calibrate radio channels...

Try connecting it like this:

Can you please say what d'you see in the mission planner radio calibration screen ? Nothing moves when you move the sticks in your radio ? Are all the sticks shown centered in the missionplanner ? Is the throttle channel shown low in there ?

Yes sir,,nothing moves when I change the sticks,,,,all values remains same,,,,nothing happens at all,,,and when I click done,,,it says BAD channel 1 input error...

Tried this one,,,not working sir...during PPM mode,,,(If you are using a PPM Receiver, put a jumper on the “S” inputs of channel 2 and 3, and connect the PPM input to channel 1)....I dont understand it sir...

Let's see:

1) Your receiver is giving out proper signals as you tested ESCs directly.
2) You can calibrate accelerometer, compass etc. so your APM firmware is working properly.

The only conclusion here is that either
1) you are improperly connecting the receiver and APM or
2) the input line on APM is faulty.

Try this:
1) Connect only receiver to APM, power up with LiPo and connect to computer.
2) While the APM is powered up, post one picture of APM + receiver and one screenshot of radio calibration window.

Ya,,,I tried the connection you have given in the image sir,,that too not working,,,now I have done as you told in the last reply and here are the images...

Can you please post one more picture of radio calibration screen with receiver wires not connected to APM ?

It could be that the receiver isn't receiving power. Rest seems fine.

Check the voltage on the inputs '+' line using a multimeter.

If Rx wires not connected to apm, how will it get powered ??
Checked voltage across I/O ports...shows around 5 V throughout,,,Lipo is fully charged....Tx also sends all values which I got checked on its display...Only problem I guess is with apm...which is not getting powered with USB alone...and may be there is a problem with apm & Rx connection...I dont understand what it means by saying PPM mode and connect Jumper on 2 & 3 S input of apm chnls...and connect PPM input to CH 1...where from PPM input Comes?

SOMEONE WHO HAVE WORKING QUAD COMPRISING FLY SKY 8 CH TX & RX WITH APM 2.6 EXTERNAL COMPASS & GPS IS SO HONESTLY REQUESTED TO GIVE ME PROPER IMAGES OF ALL CONNECTIONs ASAP.......

Can't see any problem with APM - receiver connection . I was asking you to remove receiver connections from apm, and connect it to missionplanner this was for checking whether apm detects missing rc inputs ,so please post pic of rc calibration screen with out your receiver channels connected to apm

I know this being question have been asked several times , but are you sure , the red led on receiver is staying lit , when your receiver is being powered from APM ?

Yup...red led is solid and binding was perfect...

Yes sir,,without connecting the Rx with apm,,,,in mission planner it show no rc connceted,,,,and here is the image of rc calibration screenshot

I am working on my quad. It still does not fly because I haven't got time to mount it on a frame. But all calibrations and settings are complete. Connection pix are available in my thread http://www.rcindia.org/multirotors/building-apm-2-52-quadcopter-with-st360-kit