A PA28 pilot reported a runway incursion because his aircraft would not stop before entering the runway on a taxiway covered in ice.

Narrative

We had a day of rain followed by a hard freeze and the taxiway was glare ice. I was cleared to taxi to Runway 28R but given option of Runway 28L; which was in better condition; and told to taxi via Alpha and Charlie. I asked for progressive taxi because my airport diagram did not show Charlie. However; I located Charlie and cancelled the progressive. I wasn't sure where to run up but decided I would run up on the other side of Runway 28L as I'd already been cleared to taxi to Runway 28L and didn't want to delay crossing Runway 28R. I was taxiing no faster than 5 KTS as I approached the hold-short line (which was not visible because of the ice; there was a flashing light; however). Brakes did not provide any braking action and I skidded about 2-3 feet beyond the hold-short line. I contacted the Tower on ground frequency and advised that I'd skidded beyond the hold-short line for Runway 28R. I was then cleared across Runway 28R to run-up on the other side of Runway 28R. I also had difficulty on the other side locating the run-up area for Runway 28L but did so with assistance of the Controller. I have never taxied on ice before; but I was going extremely slowly throughout the taxi in consideration of the advisory for poor braking conditions. Nonetheless; I could not prevent the skid. I was fully aware of the hold-short line prior to the incident. After the event; the Ground Controller asked me for a taxiway condition report and I advised that braking action was 'very poor.' I should have crawled more slowly throughout the taxi.