Can you program old garage door remote with new garage door opener?

You can as long as one of the following conditions applies:
- The new opener does not have a Security + feature
- The new opener has a Security + feature and the remote does also
- The new opener has a Security + feature, but it allows it to be bypassed (rare)
If you do not fit one of these categories, you can still make your remote work if you know the 9 part switch code for your remote. This code will tell you what switches to turn on or off inside your remote to program it with the correct code. The switches will be all on one panel and are located inside the remote, often in the battery compartment. Look it your instruction manual for a code. It will probably look something like this: 2|1|0|2|0|1|0|0|2. Each of these digits corresponds to a particular switch, the first digit to switch #1, the second to #2, and so forth. A 2 means the switch should be all the way up, a 1 means it should be half way up, and a 0 means that it should be down. Set the switches in your remote accordingly. Now the remote should operate the door without any further actions needed. If you don't know the switch code, you can always try all the combinations. There's only 19,683 of them.
If you do fit one of the categories, press the purple, yellow, or green learn button on the back of the opener and hold down the remote button until the light (the big one, not the LED) flashes a few times. If you don't want to get up on the ladder, this can also be done by holding the remote button, then the light button, then the open/close button until the light flashes.