Thanks everyone for the replies. We have done some more checking and
verified the two unknown pipes are NOT wastewater from other
properties. We have also verified the downspouts go to the street
gutter now (but probably did feed into these two pipes originally). My
question now is, do you think it's likely that a perimieter drain
system (under the foundation) may still feed into these pipes? A
contractor we asked told us this is quite possible in a home 50 years
old.

We cannot just connect these pipes back up to the side sewer, as the
City will not allow it, knowing the pipes are not wastewater. Even
though the downspouts no longer feed into these pipes, if they are
collecting stormwater then the discharge ends have to be connected to
something, otherwise water will collect around the foundation.