OK, the 7184 needs a constant source of 120VAC on the L1 and L2 to power that control. The LIMIT comes from the aquastat B1 and serves to 'trigger' the 7184 to fire the burner.
I have no idea how a line voltage thermostat might be wired into your system...
Start by tracing the L1 wire back from the 7184 to see where you are losing the voltage... that may be your problem... in fact, probably is... but look for that 'line voltage thermostat' too... ??
Pictures might help us... free account at
Image hosting, free photo sharing & video sharing at Photobucket , upload pics there, and drop a link here for us to view them.