It's going to depend a lot on what other hardware you have available, but here is a fairly simple & cheap idea that would work.
You will need:
PC on all the time.
Teamviewer, remote desktop, logmein, etc on PC & a phone that supports that software (I used teamviewer).
I/O card connected to PC. Fusion Brain is the one I use for stuff like this (check the support forum at Mp3car.com)
You'll either need the Cat5 ran to the PC or a USB + 12V to where the Cat5 is to power/control the Fusion Brain.
This is going to depend somewhat on the door openers, but I think they are mostly the same. I'm writing this based on my genie openers & the fusion brain. For my method, you'd need: 1 fusion brain ($60ish, for v4, you get 15 ouputs, 12 inputs, you could control 6 garage doors with my method & have outputs leftover), 2 relays, 1 cat5 per door. you could use 1 cat5 for 2 doors with some common grounding, but seems more complicated than running the 2 cat5 you already have....
Use 1 pair from the cat5 to simulate a press of the wall button via a relay. That will cycle the door just as if you pushed the wall button. You'll probably want to use diodes to keep the switches from interfering. This is 'dumb' in that you won't know if the door is going up or down, opened or closed.
To make it smart, add limit switches for open & closed. Use 1 cat5 pair for open, 1 pair for closed (some openers may have this already to be piggybacked). You can then use logic to decide if what you want to do should be done (ie-if you hit 'close door' and the door is already closed, the software ignores the command & tells you you're a dummy.). You can get as creative as you want with the logic software - run a GUI on the PC & just use remote desktop to click a button, make your own iOS/droid app, make a web GUI & expose that to the 'net, and so on.
The fusion brain just got a hardware update to v6, but the software isn't done yet (usable if you're familiar, but a PITA, IMO - C# +XML puts me off). the v4 will do all you need (and have inputs & outputs to spare) and has software available that will be easier to start out with. (if you know VB6 or .net, PM me and I'll send you some source that will get you up & running even easier than fusion MDX)