My laptop fan has starter going on/off over and over.

It sounds like the CPU cooling fan is what you hear.  Could just be something blocking air flow, could be the CPU heatsink is not making proper contact (loose), could be a bad thermal sensor, overworking it in an area that is hot or no air flow, etc - many potentials.
 
If the PC is still in warranty, contact HP.   HP is the only one that can fix it under warranty. 
If its out of warranty, and you are comfortable with PC hardware consider cleaning it out.  If not, take it to a trusted PC repair shop and have them go through it.
 
I use Macrium Reflect (paid version) for my backups.   They have a free version that many use.  Acronis is also popular and I used it for a long time before switching to Macrium last year.  Of the two, I like Macrium better. 

fireberd
It sounds like the CPU cooling fan is what you hear.  Could just be something blocking air flow, could be the CPU heatsink is not making proper contact (loose), could be a bad thermal sensor, overworking it in an area that is hot or no air flow, etc - many potentials.
 
If the PC is still in warranty, contact HP.   HP is the only one that can fix it under warranty. 
If its out of warranty, and you are comfortable with PC hardware consider cleaning it out.  If not, take it to a trusted PC repair shop and have them go through it.
 
I use Macrium Reflect (paid version) for my backups.   They have a free version that many use.  Acronis is also popular and I used it for a long time before switching to Macrium last year.  Of the two, I like Macrium better. 

Thanks Fireberd. I will look at Macrium right now. My PC is no longer under warranty. I'm not afraid to open it and blow some are and check to see if the heatsink is tight.. I'll rub a dryer sheet over my hands before I do to try to be sure I don't have any static charge. I do have a wire with an alligator clip but I wouldn't know where to hook it on a computer. I've used it on tube electronics to drain caps. I'll just be careful but I'll get the drive, software, and make a drive image before I clean it... just in case.
 
Thanks for the reply Fireberd. The air is coming out a vent on the end and it is quite warm. Ive just never noticed it cycling on and off like this before. It has been a good computer.
 
Julien
 

I'll consider it but it is 90 bucks for 4 computers, I have 3 now and will be getting another.

It doesn't have a drive in it but I am uncertain about what it will and will not do. I think I'll just buy a case and matching HD and get software that I know will work. This case should do fine for backing up some files on an older computer. It has W7 drivers available for download but I don't see any W8 drivers.
I like easy and nothing seems to be... but I'll figure it out, just not with this "one button" backup.
 
Thanks for the advice!
 
J

High temperatures somewhere in the system is a good guess. 
 
http://www.alcpu.com/CoreTemp/

Cleaned and/or replaced fans, and/or replaced screens and/or keyboards,... for at least 6 laptops this past year. A real pain. Laptops are not designed to be disassembled. Some require the screen to be removed. All of them were down to the bits.  Not an easy, quick job.
 
And: the screws are different lengths, thicknesses, color,...  And there are always more to replace than I find holes for.
 
I found lots of dog hair in one. The others were mainly dust from blankets and clothes. I always use a clipboard to support my laptops when used not on a desk.
 
One had a dead fan. I replaced both of the two fans to know continued joy.
 
Some use closely spaced fins that accumulate micro debris. This is by design. 
 
If I have to disassemble completely I will clean the chips and heat sinks and apply new compound.
 
I use a small tankless air compressor to blow dust from computers. Cans of air are too expensive and wasteful. And never contain enough to finish a job.  Good for little quick puffs when soldering,...
 
Remove the DVD drive, remove the battery (should be removed when using AC to increase battery life, and reduce heat from charging), remove all panels, remove the ram, use the air compressor to blow thru all the holes.  Use a small, long bristled brush to push thru the fan vent holes. Blow again.
 
If you need to disassemble, find the service manual on line, and search and watch a bunch of videos before you start.  Remove enough screws to remove the keyboard. CAREFUL with the ribbon connector. These can break easily if the wrong technique is used to open them. Some flip, some slide. Use a bright light and a magnifying glass to see clearly.  Blow thru the revealed holes.  Might not need to do more.  If so, remove next part, and clean again.
 
Keep the different screws in different containers and locations on your work surface. Make notes about the different screws.
 
I have an 18 inch laptop on my desk that is often running videos. The fan cycles lots when doing this.  Not so much when recording