In the U.S. ....
Your one-year warranty includes replacement coverage for a defective battery. You can extend your coverage to two years from the date of your iPad purchase with the AppleCare Protection Plan for iPad. During the plan’s coverage period, Apple will replace the battery if it drops below 50% of its original capacity. If it is out of warranty, Apple offers abattery replacement for $99, plus $6.95 shipping, subject to local tax. Apple disposes of your battery in an environmentally friendly manner.
You have to be the judge of whether it is cost effective to you. You can backup all of your app data with iTunes or iCloud and restore from the backup if you get a new iPad - and then all of your data and game saves should be restored. You should not lose your in-app purchases either as they are stored in the backup.
If you have had an iPad for almost 3 years, I would hope that you have been backing up all along. If you sync with iTunes all of you apps and other media are stored in there, and iTunes has been backing up your iPad when you sync. Paid content can be downloaded again for free (in most cases) as long as you use the same Apple ID that you bought it with.