Well yes, cancer would definitely show up in blood work!! In order to properly diagnose a brain tumor, you would have to have an MRI (magnetic response imagine) done. Oh yeah, you can check for neurological damage in most animals. There are tests that pertain to the animal's reflexes. The most common ways for a veterinarian to diagnose a neurological problem in animals is by observing their mental state, examining the animal's cranial nerves, postural reflexes (the way the animal responds to how you restrict their balance), radiology (looking for spinal trauma), and from looking at my notes, bloodwork is a diagnostic tool to!