Which OS are you using?
A few more things you can try are
1) After uninstalling, delete the trash, clear cache and cookies. Make sure it is all gone before trying to reinstall.
2) Attempt to do the download while hardwired to the internet
3) Check system permissions to be sure TurboTax has full disk access.
4) Check for security software issues blocking it. TurboTax should meet security standards, but allowing it to bypass anyways may allow you to install