Can I travel with new employer with stamped H1-B visa?


I have H1-B visa valid upto September 2015. This visa was initiated by employer A and I got the stamping done on passport. Due to lack of US openings i left employer A and joined employer B. Now employer B is not willing to transfer my visa. So my question is whether I can apply for a new employer who can use my stamped H1-B visa and make me travel to US?

If the new employer can apply then will the quota limit be applicable to me?

Please note, I have not travelled to US and right now I am in India.

Would really appreciate if any one can give me their suggestions on the same.

Thank You,