The introduction of block-based programming has gradually changed the landscape of programming education, particularly for school children. Block languages today, however, have serious technical barriers to students with disabilities. For example, block languages are generally not screen reader accessible, incompatible with braille, and contain serious problems for users with motor impairments. No student with a disability should ever be denied access to learning computer science and they do not have to be. To help rectify this, we present a new approach to the design of block languages called Quorum Blocks. Quorum Blocks uses a custom hardware accelerated graphical rendering pipeline that takes into account how screen readers and other devices work under the hood. We discuss these technical details and demonstrate that accessibility support can be fully achieved without meaningfully losing either the look of modern blocks or their visual output. We present the results from focus groups that highlight the barriers students faced with a variety of disabilities when using the first version of Quorum Blocks. We focus especially on challenges with low vision users, screen reader users, or those using no mouse and only one hand to type. Block languages built using either our techniques, or on top of our libraries, would become accessible out of the box.