How do I open my garage door without a remote from outside?
It sounds like the controller needs to be reset and the remotes reprogrammed.  Usually this requires physical access to the opener, but if you have a hardwired remote it might be possible to pair it via the keypad. Check the manual for your opener.
But back to the problem of how to open it. If the garage does not have an alternative access there should be a manual cable release which disconnects the door from the opener chain so that you can manually open it.  Often this is in the form of a small key near your garage door.  With the key you can open the lock and pull the manual release.

(source: garage-door-automation.co.uk)
If the installation was done correctly, you have one of these you just need to find it.  If you don't have the key a locksmith should be able to open it for you.
If you do not have a manual release then I think you will have to resort to breaking a window.