In terms of making more than you're currently making, I've never found it effective to tell an employer of any kind large or small what I'm making. A place like J&J definitely has its bureaucracy in place, and that means it has salary ranges predetermined for a position.
The notion of an employer pressing you for your current earnings is a brilliant disguise for laziness. It means they want the previous company to do their homework. It's really imperative for both candidate and employer to focus exclusively on the current opportunity. What do you bring to them, and how is that expressed in terms of the current job market salarywise? Then what is their range for the position, and how does it compare marketwise? Also, what about other forms of compensation, like benefits, stock options, bonuses, etc.
One other thing. It has been said that it is better to have worked for a big company than to work for a big company. At the very least, you'll get the prestige of a big name like J&J to punch on your resume "ticket" for future positions.