constant current source circuit 1550e
If either D1 or D2 are not functioning i.e. there is an open circuit in the diodes, the base current (due to the 10k ohm) will be about 1mA and, given that the transistor will be ~close to saturation, it's hFE could be about 70 and hence you get ~70 mA through the LED. 

Check the voltage on the base with respect to ground - if it appears to be about 2V then an open circuit (or reversed) diode is the problem.