HI
I received L1-B VISA with company A, but I did not travel.
I joined company B.

My question here is ;
1. If I don't travel on my Existing L1-B VISA, does it cause a problem?

2. Will it affect my chances of getting L1-B/H1-B with my new Company B.

3. As I have already been issued a L1-B , should I apply for H1-B with my new company B
(or) still should I apply for L1-B VISA with my new company B.

PLEASE REPLY.

If you want to enter US as employee for company B, you must file for L1 transfer. Employment visa is attached to the employer, you can't enter US as company A's employee and work for other company.