Car wouldn't start, Aftermarket alarm? Options

[BlackSTX]

Don't know where this should go exactly. My car wouldn't start the other day. I even replaced the battery and tried several times and it still woudn't work. So I had it towed to the dealer and sure enough it starts right up for them. They told me the only thing they can think of is that it's an aftermarket alarm system that's installed may be interfering somehow. I didn't even know it had a system since I bought it used. Anyone know if this could be right? When it wouldn't start, it would turn on, meaning the battery was good but it just wouldn't start.