My flight was cancelled but the airline offered me a new flight. Does this mean I’m not entitled to compensation?

In the event of a cancellation, the airline is required to either offer you a new flight to your destination, or to refund you for your original ticket. In addition, you may be entitled to compensation, subject to the cause of the cancellation and whether this constitutes extraordinary circumstances. So just because the airline offers you a new flight (and/or care), this doesn’t mean you’re no longer entitled to receive financial compensation as well.