Opening the DLP > Sign-In (or Watch Offline) to access the Library screen > Click Help > The version is written in the bottom right hand corner.
If it is the latest v1.0.15327.48, I would go through the following steps to ensure no corrupt files are lying around:
1. Delete the underlying 'Sky Go Player' folder for the new DLP to ensure that there is no old corrupt files hanging around. Mac users should find it in Users\<user>\Movies\Sky Go Player. PC users should find it in Users\<user>\Videos\Sky Go Player
2. If you are no longer going to be using the old Desktop Player uninstall it (on Mac right click and remove) and clear out the underlying 'Sky Player' folder. This exists alongside the Sky Go Player' folder.
After clearing out the old folders, try and download another bit of content from the website. Open and sign into the new DLP and it should hopefully download successfully.