Poor contact within the lid switch has stopped many a machine. Replace the lid switch. There's a new kit:
Regarding your pump question, there is no particular filtration device except for the tiny holes in the wash basket. The electric pump is subject to lint clogs and other issues, so if the tub does not drain within 70 seconds or less, replace the pump. Remember that the lid switch must be working properly for the pump to engage, so the test I recommend is only if you can hear the pump running.