Are you doing this for some sort of class or something?
Corporations absolutely do give money to politicians every day, it's just through a complicated endrun system.
Are you aware of what PACs (Political Action Committees) are? How about SuperPACs? How about "sponsoring" events, which happen to have political things attached to them? If a corporation wants to give money to a politician, then they pretty much are going to find a way.
Also corporations are only considered "people" when it is in their favor. You can't jail one. You can't force non dischargable debt onto them. They can be effectively immortal or die at will (whichever is more to their favor).
I imagine the courts thought the issue was a non issue except in academic circles where practicality has no place.
One may wonder why this law still exist when current campaign finance law allow corporations to partake in the political process anyway through setting up Super PACs, but there it is. This law, by the way, is called the Tillman Act of 1907, if you are interested.
I'm pretty sure he's aware of Super PACs. :p
At any rate, legally, corporations are people to ensure liability is carried with the corporation, or at least, this was the original intention under common law. For instance, a corporation cannot legally vote for the President, or run for public office (President Enron?!). Rather, as a legal person, it is permitted to act as a single individual for legal purposes, which is a big deal in common law, where only "people" could be sued historically. In other words, by extending personhood to a corporation, one opens it to legal action where limited liability - that is to say, the notion that the owners were not responsible for any more financial liability than they had originally put into the company in the first place (i.e., if they put $5 into buying a share, they can't lose their house to the bank if the corp. goes bankrupt to cover the debts) - would otherwise restrict such legal settlements. Essentially, legal personhood is itself a loophole designed around some of the aspects of common law that became outdated over the centuries ("Oh, you want to sue them to get your money back? Well, you can't since they're not a person...so we'll pass a law that makes them a person and let you go ahead."). As a legal person, it can only have such rights as it is granted and such responsibilities as are required under the legal acts that defined it as a legal person, in contrast to the so-called natural person, who is born to it by virtue of being human (usually). If this includes a recognition that any significant concentration of wealth tends to skew the political process and thus consequent steps in order to mitigate this, especially in the case of corporations that tend to make it easier to amass such a concentration, then so be it.
Or something like that.