I recently purchased a house that had two buried electrical outlets. These outlets were capped with wire nuts and heavily wrapped with electrical tape.

After moving in we realized that there other outlets that share that same wall that were not working.. Would these buried outlets cause a break in the circuit?

Could be. Best to take apart the splices, remake them, re-cap with wirenuts, and put covers on the boxes after the power has been restored to the other outlets, and do not bury the boxes. Any junction box must be accessible.