I would not send anyone into a 36" storm pipe...I think that's begging for trouble. Donating the drainage and an easement to your local jurisdiction may be the best approach for you. They may be able to rehabilitate the pipe w/out ripping the whole thing up. Options include sliplining the existing pipe with a plastic liner (HDPE) or a technique called "pipe bursting" in which a new pipe is pulled through the existing pipe. But, if it's the jurisdiction's pipe, let them worry about it (but you may have to lobby hard to get them to act soon).
Before you do ANY changes to the pipe, other than simple repairs, you'd better have a professional engineer evaluate the design hydraulic capacity of the pipe and the capacity after you do your work. (i.e., don't change the inside diameter, internal roughness, or anything that could reduce (or increase) the flow through the pipe..it may not be designed for increased flow downstream. Decreasing the flow upstream could result in flooding of your upstream neighbors. Either way, you may be liable for damages.)
Again, the best approach for you is the donation to the local jurisdiction. If the pipe drains only private property, the jurisdiction probably won't want the pipe. In that case, you'd better get with the neighbors upstream that contribute to the drainage and get their $$$$ support.
Good luck-drainage issues can get messy.