I just started a new birth control and the first week is normal along with the third and fourth. It the second week I have a dark brown discharge.?

It should go away. Irregular bleeding when first starting the pill is relatively common. I encourage my patients to stay with any new pill for 3 cycles before changing to a different pill. If you cannot stand the irregular bleeding, the next step would be to use a pill which contains more estrogen than the one you are currently using. That change may or may not help in the short term and but should help long term.