Heater core?

My girlfriend has been running water through her cooling system for almost a year instead of Dex-cool. Now she is leaking water underneath the vehicle and the passenger side floor is soaked through!
I think the heater core is to blame but, do not see fluid dripping from under the dash area when vehicle is running. And the floor seems to get wet even when car is not running.
Will the heater core leak when the car is off? And, is it possible that the fluid is running down the firewall out of view? Is a leaking heater core the ONLY way the floor could get wet from coolant?
The heater core seems like it is going to be difficult to get to and i want some advise before i begin. I'd appreciate any help you can provide.
Thank you. -J. Watts