You probably want to put a medium-value resistor from the base of T2 to ground. T2 is probably supposed to be a class-C amplifier, and without the base resistor the B-E rectification will bias the transistor to the point where is only conducts through an extremely narrow portion of the carrier cycle. Select the base transistor to give you the desired conduction angle. I don't know, start with 1K?
Also, that series-resonant output filter (L3, C6) is tuned somewhere around 5 MHz, not 27 MHz. Even if the values were changed, a single series resonant circuit like that will probably not filter out the harmonics to be ham-legal (-43 dBc, I think). But that limit only applies to transmitters delivering 5W or more, and you will be lucky to get 100 mW with this design.