Keep your voice confident. It helps to say you're considering a move into a new industry, not that you're desperately looking for a new job. If you can avoid it, don't tell people how long you've been looking for a job or out of work. Always be upbeat. Look for an opportunity to tell a joke or be lighthearted.
Nothing helps bond like laughter.
Find more connections Even if a person doesn't seem to be much help, remember to ask each person if they know of anyone else in that industry you should call. Ask if they have that person's phone number. Always ask if they have any advice for you. Most people love to give advice. You don't have to take their advice, but something they say may be helpful.