No, Microsoft and Cisco wouldn't exist because they are based on government enforced intellectual property laws.
Something people seem to be forgetting is that any change to AnCapistan is going to have to happen in the real world. You can't just invent this society as if it exists in a vacuum. Microsoft and Cisco do exist.
Remove the legal system, good luck trying to switch to other networking infrastructures or finding compatible software, when instead of IP laws they simply send their mercenaries to your house for violating their contract agreements and take your shit away.
If you don't want to give your money to a state, you're kidnapped or murdered. If you don't want to give your money to a corporation, you're forced to do without their goods or services.
In MountainMan's land in AnCapistan, if you don't pay for what you use, I'm going to take it from you, either in the form of forced labor or seizure of assets. You're free to not be here, but if you show up somehow, I'm not giving you a free lunch. Now instead of MountainMan's land, imagine a coalition of property owners defining a common border (as people are wont to do) and establishing a usage fee. Something to cover the cost of using roads, cleaning up after travellers, etc. Oh... look, we have a tax.
Who do you think is going to try to seize control of the state hardest of all other than the evil greedy bastards you're trying to stop?
That's exactly my point. In a centralized system, you have a mechanism of mitigating, stopping, or fixing abuses by the evil and greedy. Sure, it's hard, but it's easier than rebuilding a nation from the ground up. I think it would be better to revolutionize the system from within - establish accountability and instant communication, instant public auditing of any and all government expenditures, real-time voting, abolishment and reformulation of the entire tax code, outsourcing public works and maintenance to private companies, hiring private law enforcement, and so on. You see that happening in America, slowly. Why not focus your efforts and speed things up. Show people that it can be done, and why it should be done. Educational reform is happening because of Khan academy. BitCoin has the potential to demonstrate how modern commerce can work.
Why not take the best features of both instead of insisting on a 'pure' idealistic pipedream? AnCapistan has a great thing going for it. The 'capitalist' part. Market based solutions are great. Make government earn its money. Introduce competition, make politics and legislation fundamentally economic, instead of the feel-good my team vs your team bullcrap we see today.
In AnCapistan, there's no means of stopping the bastards. Might is Right. He who has the most resources wins. I just don't see that as a particularly dignified or righteous ethos.