@sfbayboy1981-0 each ISP has their own firewall settings that block incoming connections based on different criteria. The ISP and server firewalls are not the only culprits here, as each peer has their own set of firewall rules and, in addition to that, each peer's torrent client has its own policies regarding to how incoming connections are treated.
Having a different DNS might result in the connection performing a different route that will go through different servers (thus different firewalls) and this could impact on the success (or failure) of the connection. With VPNs it is exactly the same principle, a different route, but this time much more aggresively different. Both leads to the same outcome but have different probabilities of having a positive effect.
Overall switching your DNS provider or using a VPN migh end up clearing the way for connecting with peers that otherwise you wouldn't be able to, but the opposite of this is also true, this might end up blocking you from connecting to peers that normally you would be able to reach.