No uC expressed or implied.
If you can get by with only binary-increment time periods (1 min., 2 min., 4 min., 8 min., etc) rathere than decimal (1 min., 2 min., 3 min., 4 min., etc.) then I recommend a CD4060 for the entire circuit. It is an oscillator and 14 stage binary divider, and has an asynchronous reset. With the right timing components, the high order output bits would be 1, 2, 4, 8 minutes. A dip switch selects which one to send to the computer as the reset signal. The HD signal goes to the 4060 reset.
That is the core circuit. Separate from it are the input and output signal conditioning. For example, the HD activity LED signal might need to be boosted up to logic levels to be recognized by the 4060. Similarly, the 4060 output might not be the correct logic polarity to drive the computer reset. What do you know about these two signals?
ak