Don't have access to online scores on new PC

This is just a guess, but I suspect that there is no data in the Cloud Scores folder on your new laptop.

On Windows the MS4 folder structure looks like this:

My understanding is that syncing between computers with cloud save isn't a thing yet, but is in the works. For now, cloud save just saves to musescore.com (with a local copy saved to the Cloud Scores folder DanielR mentioned). To open those saved files on a new computer, you would have to go to the website and download those files. I'm a little foggy on what happens if you cloud save again from that new computer. It definitely wouldn't update the file on the previous device, but I'm not sure whether it would overwrite the website copy or create a new one.

Cloud save as it is now is mostly useful to speed up the sharing process if you want to publish your scores. For syncing between computers, my current strategy is to save to a OneDrive folder.