What should I do about my half-dead tooth?

See your dentist. In dentistry, there is really no such thing as a "half-dead" tooth. Factors that a dentist will determine are if the tooth requires root canal treatment and can be successfully restored. If the tooth cannot be successfully restored, they will recommend removal with replacement by dental implant and crown.
Discuss your options. One has to assume that you have already seen a dentist for that diagnosis. Regardless, the only way to properly answer that question would be after evaluating the tooth, the supporting structures, the adjacent & opposing teeth as well as many other factors. You should consult with a dentist whom you trust, discuss all options, the pros & cons of each, in addition to each prognosis. They you decide.
I had this problem.. A root canal was tried but the tooth was already too far gone. It hurt all the time until i had an extraction. Fortunately mine is toward the back (molar). It has been great since the extraction.
Half dead ? Can't say if the tooth is restorable or not without a radiograph. So, your choices are to restore it with root canal therapy, a post and a crown, or extract it. Choice is yours, but remember that replacing a missing tooth is more expensive than restoring it in the first place.