Did the samething sorta with my exchange server in CT. I was thinking to move my "server" - (it's actually Virtual - Hyper-V so it's easy to just copy it to a USB HDD and go) but ended up just doing a MX backup service since ours is only shorterm.
For you, i'd try bringing the modem and Cisco routers they give yout o your house and see if they can connect. If so then it's easy to connect your Exchange to it as your IP follows the modem's MAC.
If that doesn't work you can do what has already been mentioned which is placing OOLs SMTP servers in Exchange as a SmartHost (Send Connector) in ESM. From then on mail will come to your server directly as long as you have port 25 unblocked (Boost+ and Up) and sending mail will use OOLs SMTP sever.