Where a councillor has a declared interest which prevents him/her voting, that individual is not counted as "present and voting" for the purposes of that agenda item. So, if say your quorum is 3 and you have 3 councillors in attendance and one has declared an interest preventing them from voting, you have no quorum for that agenda item so there can be no resolution. In such circumstances, it may be prudent to grant a dispensation to that councillor to allow the business of the council to be carried out. If appropriate you could defer a decision to the next meeting.
If, on the other hand, you technically only have one vote for a resolution because everyone else has abstained, then that one vote carries the resolution. Frankly, abstentions are pointless.