Getting a programmable remote is one way to solve the problem but the functionality and locations of the keys may not be satisfactory.
Repairing your remote should give you more satisfaction as you get to keep the remote you are used to.
Common faults are: some buttons not working, not working at all, corroded battery terminals. Often buttons are sticky because of some dirt accumulated over the years from the sticky little hands of your kids?
The hardest part of repair is often to open the covers. You do not need much experience in electronics repair to repair a remote. Also it is perfectly safe as there is no way to get an electric shock as they work with batteries.
Step 1: Test your remote with Digital Camera
Step 2: Open the remote control but there is a catch or a few catches.
Step 3: Take a picture of every phase so you remember how to re-assemble
Step 4: Pull everything apart
Use a small plastic takeaway box or similar to store the bits so you don't lose parts.
Step 5: Inspect the circuit board and repair dry joints
Sometimes I have washed the circuitboard with soapy warm water, good rinse after that and drying with a hair dryer. I would not recommend the same treatment for you cellphone as some components do not like water.
Step 6: Wash the covers and the buttons
Step 7: Rinse, drain and dry the parts
Step 8: Repair case and re-assemble
Re-assemble bits in reverse order and make sure you have the buttons in right place and right way around. Small nicks and dents on plastic cover can often be repaired by heating carefully with a hair dryer. Do not use a lighter with a flame as it is too easy to burn the plastic. May be you can get rid of some dog bite marks on the remote if they are not too deep?
In case of lost fallen out IR LED you can use second hand LED out of other remote you no longer use or buy one from Electronics hobbyist supplier. Make sure you get the polarity right or you need to get another one.