Default [Q] Broken Screen, Trying to Recover SMS & App Data

First time poster, I apologize if this post is a mess.

I recently dropped my Droid Charge down a flight of stairs. The phone itself still seems to work - I can boot it up, it plays all the proper sounds, and my 7pm alarm even went off today (hadn't had it on to test that before), but the screen is completely dead.

I've already upgraded to a Galaxy Note 3. I had a backup with SMS Backup & Restore from April; same for my Checkbook app - these are the two apps I'm most concerned about. I'd like to get the additional data since April 22.

My Charge is rooted, though I got a lot of walkthrough to do it - I also did the root over two years ago.

I have these links in the chatlog with the friend who helped me root, if that helps at all:

Problem: USB debugging was turned off when I dropped the phone. I didn't know any better until I'd already broken the screen. I've tried MoboRobo, MyPhoneExplorer, and Samsung Kies, and nobody sees the phone. It beeps when plugged in, and with Kies the hard keys light up about ten-twenty seconds later, but that's the furthest I've gotten.

I'm willing to boot to recovery and use adb/command prompt/whatever, but I can only find these instructions for other phones, and I'm worried that if I use the wrong phone's menu instructions I'll end up wiping it instead of booting to recovery. I'm also not too clear on if ADB is a different build for different phones... this is my first time doing this.

I don't have a mini-HDMI cable but if that's the better solution I'll get my hands on one.

Any help is appreciated, thank you!