Would the following touchscreen control panel be compatible with your service?
Vivint Sky Control Panel
Also, is it possible to tell if this is a Verizon or and AT&T Panel?
There are no Alarm.com Cellular Modules for that control panel. If your sensors operate on the 345Mhz frequency you can use a 2GIG panel to communicate with them. This would require a new panel and a new cellular module.
You could get the 2GIG Go!Control GC2 with either a Verizon or an AT&T module. Here is a tool you can use to check which of the two carriers provides the best machine to machine cell coverage in your area.
If you decide to sign up for service, this guide gives a comparison of our Basic Interactive and Gold Interactive Packages. Keep in mind, if using z-wave devices for home automation, you will need to sign up for the Gold Interactive Package.