(a) All actions against physicians, surgeons, dentists, medical institutions, or other health care providers for liability, error, mistake, or failure to cure, whether based on contract or tort, must be commenced within two years next after the act, or omission, or failure giving rise to the claim, and not afterwards; provided, that if the cause of action is not discovered and could not reasonably have been discovered within such period, then the action may be commenced within six months from the date of such discovery or the date of discovery of facts which would reasonably lead to such discovery, whichever is earlier; provided further, that in no event may the action be commenced more than four years after such act; except, that an error, mistake, act, omission, or failure to cure giving rise to a claim which occurred before September 23, 1975, shall not in any event be barred until the expiration of one year from such date.

(b) Subsection (a) of this section shall be subject to all existing provisions of law relating to the computation of statutory periods of limitation for the commencement of actions, namely, Sections 6-2-1, 6-2-2, 6-2-3, 6-2-5, 6-2-6, 6-2-8, 6-2-9, 6-2-10, 6-2-13, 6-2-15, 6-2-16, 6-2-17, 6-2-30, and 6-2-39; provided, that notwithstanding any provisions of such sections, no action shall be commenced more than four years after the act, omission, or failure complained of; except, that in the case of a minor under four years of age, such minor shall have until his eighth birthday to commence such action.