Hi Trevor,
The circuit should work fine with your 4.8V supply. Anything more than 7V will exceed the absolute max voltage rating of the 74LS73.
When the output of the 74LS73 goes low to 0.5V or less. the base of the transistor will be pulled down to about 4.0V. The 680 series resistor will have at least 5.2mA through it and the transistor's base will get at least 4mA. With each segment of the display very bright at 30mA, seven of them draw 210mA. Therefore the transistor must have a current gain of 210/4 = 53. Its guaranteed minimum is about 60.
Typically, a BC327 will saturate at 0.25V with a 210mA load and 4mA of base current.
Maybe you have its emitter and collector pins reversed.
Maybe you have a weak BC327 transistor. General Semi sell them in batches of selected current gains and their BC327-40 has lots of gain. :lol: