Can I use a Mac mini without the power brick?
If it's a 2005-2009 model then NO! You absolutely cannot plug directly from a AC power source to a computer that does not have a built in transformer power supply, which the Mac mini 2005-2009 model does not have.  The AC current must be converted to DC current first and that is what the Mac mini's power supply does.

Starting in 2010 the Mac mini used a built-in power supply and the power cord does not use a power brick like in previous modles, it plugs directly from wall to computer.