Transistors, explanation of current gain
The problem here is that your transistor is no longer in forward-active mode, but in saturation. The equation \$I_C = β·I_B\$ is only valid in forward-active mode.

When the transistor is in saturation mode, the equation to use becomes \$V_{CE} = V_{CE,sat}\$, and the transistor acts like (to first-order approximation) a voltage source. If all you care about is \$I_C\$, you can ignore the base entirely since you don't have anything in series with the emitter.