Recently, I have been fired from a job that I held for three and half years. I had requested medical leave in order to have surgery to remove a large tumor, requesting a six week absence. Complications arose two and half weeks after the surgery, which resulted in not one but two more surgeries in order to remove cancer from my body. The company handbook stated that they will only allow for six week absences, however the first and third surgeries each required, at least, six weeks of healing time. I notified the company ahead of time and they were unwilling to work with him, resulting in my termination as I was going in for my third surgery. Do I have a case against them or do I, at least, have a good case for unemployment? My job was located in Kentucky, if that helps.

Is your company large enough and does it fall under the FMLA
( federal laws on medical and family leaves) if so they would have been required to give you this time.
If they do not fall under that program, they are not required to give you the time beyond that of the company rules.

I agree, if they qualify FMLA would govern this issue. Family and Medical Leave Act (FMLA)

The company is a national chain, so it's large enough. They only gave me six weeks of medical leave though.

Many of these chains will never tell you about the law, a lot of managers don't even know about it. Should be a large poster hanging in an employee area.

Contact the corporatoin HR department

FMLA allows qualified employees 60 days (12 weeks) of absence. This time runs concurrently with a medical leave. Sounds like you were off work for more than that amount of time in a 12-month period.

You say you asked for medical leave, were you granted leave under FMLA? The company handbook may say no more than 6 weeks but FMLA rules this issue and the company could possibly be in violation. Could be worth your time to contact a local labor board. Have you appealed to the company's HR department?