I've installed 6.0 and 6.1 and 6.2 beta - all with no problems, so your issue might be environmental. Do you have installation permissions in your environment (including installing a new Windows Service which Blue Prism will do)?. Are you overwriting an existing installation - if so it might be worth trying to uninstall that first or ensure you are installing v6.1 (v6.0 was not for upgrades)? Are you installing the correct version of BP for your environment (64bit version for 64bit environment)?
Beyond those questions - the product support team is probably going to be your next stop.