I have repaired a quite a few faulty remote controls and most often they are repairable.
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

Check your batteries first or buy new batteries. Once you have good batteries, you can test with a digital camera by pushing the buttons and having camera on and pointing to the infrared led. You should see red light if the remote is working. If no light comes up you obviously have a dead remote but do not despair and procede to the next step

Step 2: Open the Remote Control But There Is a Catch or a Few Catches.

Remove the screws if any. Sometimes screws may be hidden under a sticker or rubber feet. Often there are no screws at all but just plastic catches hidden so you have to be clever to open it without breaking the case. Use something blunt and flat toclick the covers open. This is often a challenge but should not be too difficult.

Step 3: Take a Picture of Every Phase So You Remember How to Re-assemble

Since you are using a digital camera you might as well take pictures of the disassembly so re-assemly will be easier.

Step 4: Pull Everything Apart

Did you take a picture of the keyppad layout? Sometimes keypad is just one rubber membrane but sometimes the keys fall away like pieces of a Lego puzzle. And if the buttons are marked with numbers and functions you may struggle to re-assemble them in right order?
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

Remotes are often dropped on the floor and may develope dry joints on the battery contacts or circuit board. Inspect the contacts and circuit board under good light with a magnifying lense or if lucky you might have a microscope or just a very good eyesight? Solder all suspicious joints. If there is a sign of water damage you can use methylated spirits and toothbrush to clean out the circuit board.
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

Use a smal bowl or similar to wash and contain all the parts so you don't lose bits down the drain. Use old toothbrush to clean all button holes and buttons. Warm water with dishwash liquid does the job. Take particular care with those small buttons and clean them properly. If you can leave the bits to soak overnight they come clean easy. Ultrasonic cleaner would be good for this job but most people do not have one in their cupboard.

Step 7: Rinse, Drain and Dry the Parts

Rinse with warm water. Use a drainer to contain all the parts without losing small bits down the drain. As extra security use sink plug. Dry with a paper towel. Wipe the buttons dry individually as they may still have some dirt which makes them sticky when in use.

Step 8: Repair Case and Re-assemble

If there is damage to the case or buttons you need to do the required repairs. Use hot glue or super glue depending on fault. Let dry overnight if you had to glue something.
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.

Step 9: Test With Digital Camera

Test every button as before. Sometimes you have to push two remote buttons simultaneously as with recording buttons on my Panasonic VCR.
Once you have completed test with your camera you can use the remote. Thats it, I hope you got it going again?