A couple corrections to keep in mind here.
Rottendog does not use transistors for coil drives, they use FETs. The original Williams design used TIP102 and/or TIP36 darlington transistors.
To determine if a trans or a FET is bad, it's best to use the diode setting of your meter (not ohms.) Center leg (metal tab) on a FET or TIP gets the black DMM lead, red DMM to either leg. For TIPs you should get .4 to .6. On FETS i can't remember... just check it relative to the FETs next door. Different values indicate a problem.
Also HS2 does not have a coin door coil power interlock switch (that started with Twilight Zone.)
The new replacement transistor from Marco will work, but it's not as robust as the original. It can sink 16 amps, where the original can sink 21 amps. Not that it matters, but i always go with IRL540 transistors myself as replacements.
Also this all happened because you installed the new Rottendog board without replacing the original coil first. If the coil was shorted (which no doubt it was, due to the smoke), that will immediately fry the driver TIP or FET. So that's why this happened. It's always a good idea to check coil resistance with your meter when in doubt. Anything below about 5 ohms (this is a 50 volt game, 30 volt games can go a bit lower), and you need to replace any given coil.