My HP Pavilian a6750y tower when turned on fan runs , but no light on powere button and moniter is blank

Indicates you have a bad Power Supply, to me.
Weak voltage power rail.

1) ALL of the LED lights combined use less than 1 Watt of power.
2) EACH fan uses 2 to 3 Watts
3) A typical Processor can use 51 to 125 Watts.
Depends on what Processor it is.

(The Pavilion a6750f uses an ATX power supply, that has a maximum rated wattage of 300 Watts.

http://h10025.www1.hp.com/ewfrf/wc/document?docname=c01619697&lc=en&dlc=en&cc=ca&lang=en&product=3872428#N934

The AMD Phenom X4 9650 processor can use up to 95 Watts,

http://en.wikipedia.org/wiki/List_of_AMD_Phenom_microprocessors#.22Agena.22_.28B2_.26_B3.2C_65_nm.2C_quad-core.29

(In the chart under the heading TDP)

Enough power to spin fan's, but not enough to turn the Processor on.
Not enough to also light that Power On LED light.

No Processor operating = No Video Signal from the computer.
Hence the monitor is blank.
(No Signal)

http://h10025.www1.hp.com/ewfrf/wc/document?docname=c01356113&tmp_track_link=ot_recdoc/c01619697/en_ca/c01356113/loc:3&lc=en&dlc=en&cc=ca&lang=en&product=3872428

NOTE*
Computer unplugged from power.
Anti-Static Precautions observed.

Anti-Static Precautions:
Your body carries Static electricity.

Static will fry out (Short Circuit) the hardware components inside a computer.
(You may not even see it, or feel it)

Computer unplugged from power, computer case open, working on a table;
TOUCH the metal frame of the open computer case, to relieve your body of Static.
Should you leave your computer in the middle of working on it, upon your return be be SURE to Touch the metal frame again.