If you look at the top of this section (8300) you will see a sticky that has the latest OS for the 8310. The latest is version 4.5.
However, I am not sure that will do anything to fix your problems. From your description, it appears that you may have damage from either dropping the device or from moisture.
Have you tried a battery pull to see if that does anything?
What applications do you need? If you have a Blackberry dataplan, you can go to BB App World (if access is allowed in your country).