The short answer is probably not. Most gym memberships include a clause(s) regarding liability for injuries sustained while engaged in gym activities. The clause typically provides that a member cannot sue for negligence when injured during an activity except if the wrongful act is reckless or grossly negligent. The New Jersey courts have upheld these clauses and dismissed cases against a gym when the injury occurred during the normal use of gym equipment or engaging in gym activities. So in the case of the treadmill, unless it can be proven that the gym engaged in a reckless or grossly negligent (both very difficult to prove) manner, you cannot sure for your injury.
Some of the clauses go as far as to state that the gym cannot be sued for any injury that occurs on their premises. In one recent New Jersey case, a member was injured when he fell on steps going to the pool area because the steps did not have the correct slip resistant tread. The contact had a “hold harmless” clause for all injuries occurring on the premises. In that instance, the court did not uphold the contract provision as the steps were not gym equipment. So in some instances it depends on the facts of the case to determine if a lawsuit against the gym is possible.