Would you recommend that I detach the downspout that drains below ground and attach one that extends 4-6 feet above ground? Who would I call to access the problem?

I would disconnect the downspout from the below grade drain, if I experienced dampness in the area of the basement near the downspout. The only other reasons to disconnect the downspout are to prevent floor drain backup, and to do your civic duty.

In many 1930s homes, the downspout discharges into the basement floor drain above the trap. Sometimes, leaves and other debris in the gutters can make their way down the downspout and plug the basement floor drain. This will flood the basement. (I speak from personal experience.)

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Many municipalities would like you to disconnect the downspout from the drains, because it decreases the burden on the sewers.

If you choose to go ahead, it is a job that can be done by any handyman. The downspout is cut, and elbow is installed, and an extension is installed. The below grade portion is simply capped.