Pothole:
The black flexible cable that you describe is called a "tension cable" by Porsche, and is easily replaceable so long as the attachment points under the rear main bow and at the lower end where it presses on to a steel ball have not broken off.
Its purpose is to keep the rear main bow pulled down, under tension, when the top is closed and latched.
There is a means of adjustment, which is a 14mm bolt that is visible in the area where the tension rope is pressed on to the steel ball at the tension rope's lower end. Turning the 14mm CW will reduce the tension and vice versa for CCW, IIRC. The one you describe as "missing" may have broken off if it was under too much tension.
The more potentially expensive problem (and I mean REALLY expensive), is the point at which the steel ball to which the front pushrod's plastic ball cup attaches. That steel ball has a threaded rod inboard of it, onto which a thin nut is screwed on, onto a lug at the base of the B-Pillar. If that lug breaks, the replacement part costs over $2000. The old one normally cannot be welded on or repaired easily (or at all) as the frame material is magnesium.
If you place the top in the service position and operate the top manually (after disconnecting the two plastic ball cups), you can get access to that thin nut so as to tighten it. The threaded rod inboard of the steel ball has two "shoulders" that allow you to hold it/turn it with a thin open end wrench. It would be a good idea to coat the threads with some Loctite to prevent it from loosening up in the future.
If you need plastic ball cups and don't want to pay Porsche its extortion money for complete pushrods, send me a PM and I'll send you the info on a guy who has had the plastic ball cups manufactured.
You also have to determine what caused the V-lever to break. The electric motor is powerful enough to bend it and break it, but something must have gotten jammed to cause that kind of damage.
Since you have a '97, be sure to check the mounting bracket/sheet metal under (outboard of) the transmission on that side, to make sure it has not sheared away or gotten bent out of shape. This point was reinforced on later Boxsters, but if yours are bent out of shape, the V-Lever will not be situated in a completely vertical plane and will cause you further difficulties. Examine the inboard face of the transmission (after removing the V-lever and thin black plastic plate) to determine whether it is completely vertical.
BTW, the convertible top will operate with only one front pushrod/plastic ball cup intact and attached, but it will lurch forward/lag behind depending on its direction of travel.
While you are checking everything out, check for any rips or tears in the foam drain trays. These are easily damaged by "dangling pushrods" and will then allow rain or wash water to intrude into the cabin. The water will then promptly find its way to the Central Alarm Computer under the driver's seat and again potentially cost you big $$$.
You should not have to pay anybody to effectuate this repair if you are reasonably DIY inclined.
Regards, Maurice.