I had an adsense account which unfortunately got banned. I got another but that one too got banned very soon [even though I didn't add any of my old sites to it ].

I now want to get a new account in my business name [the previous 2 accounts were in my name]. I will have a new hosting solution and a new set of sites. Will it be okay? I am worried about my IP and system may still be tracked? What all do I need to ensure so that this new account will not be banned?

I think your IP got blacklisted.

There are many factors to consider,

1. what kind of sited to you create.
2. how old are your sited before applying for the adsense account. Two months ols sites are the best.... then have a consistent posting of content. not spammy.
3. Do you ever click on your adverts; hope not.

- Google is very strict for the sake of the clients who advertise with them thus you have to comply to what they want... no option