Consideration when switching from 2N3904 to MMBT3904
Here is a comparison of the pinouts: 



Maybe you assumed the pinout was E-B-C on the SOT-23 package. Sounds like you have a forward biased junction between what you think is the collector and what you think is the emitter, so the base must be connected where the collector should be and either the emitter or collector where the emitter should be. 

So either base and collector are swapped, or all three are mixed up.