The phone is on but the screen wont cut on

Before doing anything else, I suggest removing the battery while the phone is on ---which will obviously turn it off ---wait about 10 seconds, replace battery and turn on the phone. This probably won't work, but it is worth a try for almost any problem that isn't easily resolved on a cell phone.
The phone could have a defect that is covered by a warranty or insurance (if you have one or both.) However, if this is caused by water damage or other physical damage (like the phone was obviously dropped) it will not be covered and you will probably need a new phone.