If a corporation wants to run a media campaign on social issues - that's fine. But if an ad features a politician, especially leading up to election, that'd be treated as illegal political ad.
The legal way to do is through legal lobyist. Companies can pay them and certified lobyists can talk to institutions/individuals/parties. But meetings are semi-public and the public is +/- aware of what is lobying what. Lobyists can't give gifts to politicians, otherwise they risk their license.
There's a workaround though. Politicians love to establish NGOs, then corporations donate to NGOs and politicians go on speaking tour in the name of NGO to cash out. But at least that limits use of corporate money for over-the-top election campaigns.
Well the problem is that "running media campaigns" is the vast majority of what political donations are spent on. All the other stuff (campaign salaries, etc) fits easily into any candidate's totally-aboveboard-donations revenue account.
Not saying I approve of the current system; just that this is not a problem with an easy fix.
Of course it's not a 100% fix. But it's a step in a correct direction.
edit: thinking more, it may be complicated in US where X always means party A and Y always means party B. Here we've a bunch of overlapping parties and there're multiple parties (or factions) behind pretty much any issue from any angle.
As for political donations - one of the best things in my country is that non-personal political donations are banned, period. And personal donations are capped. There're safeguard to prevent bums from suddenly getting lots of money and donating that too.