If somehow, in a parallel universe, we were to have the networks give a specific amount of free time to candidates, and the candidates could otherwise not receive any explicit or implied contribution from a corporate lobbyist (and we were somehow able to enforce this), and we could also stop the train from Congress directly into Lobbying positions upon electoral defeat or retirement, would we achieve an uncorrupted Congress?

I think we would not.  Politics is still politics, and the lying, hypocrisy and emotional manipulation of the voters would still take place during elections and during terms.  Even if Tom Coburn is not getting paid vast amounts to delay and kill Democratic legislation, he would still presumably try to do so on ideological or political grounds.  The Right would remain thoroughly ignorant, extremist, intractable and underhanded, because that is who they are--they'd make a life out of despising Liberalism for _free_ if it came to that.  Just for the love of winning every argument with inferior debating points.  And the Democrats would remain weak, trying to dryly parse nuance and ponder hard choices to an electorate that is conditioned to want the delicious empty calories that Republican salesmanship would offer.  In addition, most of the electorate would still be ignorant of the issues, depending on a worthless media that doesn't tell them anything close to the truth, and localized advocacy groups (church groups, unions, their poker night friends) would still be filling their head with fear and misinformation and misdirected anger.

Wouldn't corporations just find other means to influence outcomes, if they couldn't pour money into a campaign or lobby a candidate?  If Boeing could convince me through their regular advertising that the US was in grave, immediate danger and that the only way to stop our imminent destruction was to dramatically increase the war using the magnificent, fail-safe line of Boeing products, they wouldn't need to funnel a penny of money into a campaign--I would vote for whichever candidate was more on board with "saving America through Boeing".  Anyone who chose to campaign for increasing the war could do so simply because it would get him MORE VOTES by playing on fear than on level-headedness.  Boeing successfully influences the mindset of the electorate, that candidate wins and supports legislation favoring Boeing, and no public campaign financing laws are put into any peril.

We aren't just dealing with people who are corrupted by the system.  They are also a bunch of power-hungry, unscrupulous, reactionary, decrepit old men (with maybe 20% exceptions).  Surely the Democrats could find a way to still pathetically squander their majorities, and surely Republicans could find a way to still piss all over the citizenry in an attempt to assuage the super-rich.  What we need is a more informed, more serious populace, and a few candidates that actually can think independently under pressure.  Fixing the system, as impossible as that itself sounds, is not even enough...we have to change the underlying CULTURE that votes based largely on puffs of frivolous colored smoke.