Can Changing A Pill Brand Halfway Though My Pill Cycle Affect Whether I Can Get Pregnant?

It depends upon type of pills you are using. There are three types of pills used for birth control. These are

1. Monophasic pills which contain one hormone. (one color tablets)
   
2. Biphasic pills which contain two hormones. (Two colors tablets.)
3. Triphasic pills which contain 2 hormones and and iron supplement (three colors tablets).

If you replace a monophasic pills by monophasic pills, then you are protected. But if you replace a monophasic with biphasic then there can be no protection and many complications. If you replace biphasic pills by a biphasic pills in the mid of cycle and start the new pills from the progesterone tablet section then you can be protected. But if you start the new pills from the starting tablet then many complications. Same is true for triphasic tablets as the last 7 tablets are not related with protection.