Remote Desktop Real head scratcher.

Hello all, I am a facilities guy in charge of all IT on a grade school and church campus. I recently had installed a new phone system that I can sign-on remotely with Remote Desktop Connection. I have no problem signing on from my home and the company whom installed the phone system has no problem also signing on.

However when I try to remotely sign on using the same ip address from my work computer I can not sign on. A message pops up asking me if the computer is on. Am I using the right ip address blah, blah, blah. Answer is yes to all.

Some back ground info. I have two RCN cable trunks coming into the building. So I have two completely unique networks. One is for my school and the other is for the church offices. I have trolled the wonderful web for days and no matter what I try nothing works! I am a bit frustrated! Getting back to my issue. I have tried signing on with one win7 computer(mine, which is separate from the church's network) using the school's RCN modem. And also tried 3 other win8.1 computers from the other and separate RCN modem. This is the network I am trying to sigh on to. Is it possible to sign on from remote desktop from the same local network? because I can sign into the phone system using the local ip address on those three computers. Sorry I'm getting a bit convoluted. Still thinking things through.

I always get the same message. Asking me if the computer is on. Am I using the right ip address blah, blah, blah.
The local in-house ip address works fine. But I want to be able to go into the system remotely from my office. Which I can't.

Thanks for any ideas.

Is the work network protected by a firewall? If so, does that firewall block Remote Desktop Connection traffic?