Sounds like it's pretty far gone and only drastic measures will find out what the problem is.
I don't know what the Samsung backup/restore capabilities are like but if it was mine I would back up all contacts and personal data such as photos and do a factory reset and see if that sorts it. If not then it's likely a hardware issue and not much you can do about it apart from taking it to a phone shop and see what they say.
If it works okay with nothing on it then restore contacts, photos, apps, etc.
Not sure which network you are on but they usually have instructions, Vodafone are below:
http://support.vodafone.com.au/articles/FAQ/How-to-restore-factory-settings-on-the-Samsung-Ace