A DHC8-100 Crew did not level at their assigned descent altitude because of a distraction caused by the propeller de-ice not shedding its ice and the resultant asymmetric propeller vibration.

Narrative

While climbing through FL180 to our assigned altitude of FL230; my First Officer and I noticed that we were accumulating about one quarter inch of clear ice. All de-ice and anti-ice equipment was on. Upon reaching FL230 the props began to shed ice. However; the right propeller did not shed it completely and as a result the aircraft began to shake violently. We checked the system indicators and ascertained that the system was working. We also called maintenance and they confirmed that the system should be working as we described. I began to cycle the props from low to high RPM in an attempt to shed the ice; but this did not help. The temperature at FL230 was -35 C. We decided to descend to a lower altitude and warmer air. We informed Center of our situation and requested 10;000. We were immediately cleared to that altitude and were told by the very helpful controller that we could have any altitude we needed. During the descent the First Officer was busy flying and I was busy working the prop levers; still trying to shed the ice. Around 16;000 and -20C the ice began to shed nicely so I requested 15;000. Upon reaching we leveled off and were immediately asked by the controller why we had leveled at 14;400. We realized that we had failed to get and set an altimeter setting for the descent below FL180. The controller immediately gave us one and offered an altitude block of 14;000 to 16;000. The props were soon clean and we continued on our flight without further incident. ATC notified us of the deviation In a word; distraction. The aircraft was shaking and we were trying to figure out and fix the problem.