Ibook Switches itself off when moved - Please help!!

My ibook g4 (about 15 months old) switches itself off when i move it. Then have to force turn off (holding start button down for 10 secs)
I then have difficulty turning back on, in that most off the time the fan just starts, with no startup noise, and the computer just doesnt turn on except the fan. after a few tries it eventually works, but its hit and miss.
its my first mac, and i'm really scared something major is wrong that will cost a fortune to fix.
Any ideas??
thanks

thanks,but still unfortunately none the wiser!

My battery is definitely in properly, and it happens on mains too.
i guess i will have to take it in to the apple shop, seriously annoyed though, i loved my mac, and bought it as i thought they were reliable, however now not so sure, as i have also had 2 faulty i pods too, so am very anti apple at the mo! lets hope they can sort it out for me and redeem their reputation!
thanks for all your help, and if you have any more ideas please let me know!