EMB-145 Captain reported after maintenance action; parking brake failed after gate pushback; resulted in collision with tug.

Narrative

My crew and I reported for duty at XA:54L in ZZZ. Our aircraft; was coming in from ZZZZ and we met the crew at gate at approximately XB:00L. Upon deplaning; the Captain informed me that the parking brake was very difficult to set and that he had written it up. Maintenance showed up to the aircraft before my crew was allowed onto the plane; as it had to be searched first since it came from Canada. By the time we were allowed onto the plane; the maintenance crew was already working on it. I was able to get into the cockpit to begin my preflight preparations for our flight to ZZZ1. I noticed that the Maintenance workers were continuously pumping the parking/emergency brake up and down many times in an attempt to lubricate the lever. This apparently bled all of the pressure out of the parking brake accumulator; as evidenced by the illumination of the 'EMRG BRK LO PRES' caution light. I referred to the QRH regarding this caution light and it only said that the emergency/parking brake performance may be degraded and to use wheel chocks when parking the airplane. However; I knew to accumulator would recharge once the engines were started.Upon pushback from the gate; we were given the signal to start the engines. I instructed my First Officer to start the number 1 engine; which is standard operating procedure. Shortly after the engine started; and while the ground crew was still pushing us back; the 'EMRG BRK LO PRES' caution light extinguished; as I knew it would. Once the pushback was completed; I received the signal to set the parking brake; which I did (the parking brake light illuminated as well). However; once the ground crew disconnected the tug from the nose gear; the aircraft started slowing moving forward. I was unable to stop the aircraft in time before it made contact with the aircraft tug. Why the aircraft moved forward with the parking brake set is something I am unable to explain. My guess is that even though the caution light extinguished; there wasn't enough brake pressure in the accumulator to keep the aircraft from moving. There is also no indication in the cockpit regarding parking brake pressure.After contact with the tug occurred; maintenance was called to the aircraft and we were then towed back to the gate. Passengers were deplaned and the aircraft was shut down. A write-up was entered into the aircraft logbook and the crew was given another aircraft to continue the flight to ZZZ1.