You may have overheated and ruined the 24vac transformer. This is the control voltage that energizes the controls of the system. Assuming you made good splices, verify you have 24vac available. An electronic thermostat might not have been happy, either depending on how the cut happened (it could have shorted things together). Note, many electronic thermostats have batteries in them...check yours to verify they are still good. On some, the batteries are only for backup, on others, they actually run the thing. A mechanical thermostat won't have that problem.