Do the speakers play a sound when you start? If so, what sound is it? Pleasent musical chime (= normal)? Breaking glass/car crash sound (= problem)?
If the computer has been stored off wall power, it probably has a dead PRAM battery (user-replaceable). The following can help in the case of a dead battery until you get a new one
1) See if it will start with the SHIFT key depressed.
2)If that fails to work, press and hold this key combination:
command-option-p-r until you hear three normal startup chimes, then release the keys. You may want to figure out how you will hold all four keys before starting it.
Post what happens. If you cannot get it to start, look on the bottom or back of the case. Often there is a label showing processor speed, hard drive size, and amount of RAM originally installed. It may be embossed into the plastic. If you find a code starting with "M" followed by four numbers, that can help us identify the model iMac you have.