I tried renaming the machinarium.sol file to machinarium_save.bin but it didn't work. Presumably the data is saved in a different format.
Does anyone have any suggestions?
I don't know if any of this will help, but... maybe... you've likely already done the going to the Machinarium folder: "C:\Users\Uxxxxr\AppData\Local\Packages\Machinarium ........." & right clicking on the folder, & then on 'Properties' bit to get more info, but have you tried the 'Scan for deleted files' option that's in that same right click menu? Might... a big might... tell you if the files are gone. If you think they may well have been deleted or removed, may I suggest downloading a very useful free program called 'Recuva' - a file recovery program, it rescued all my lost emails that Windows Live had mysteriously deleted for some reason so it worked well for me:
http://www.piriform.com/recuvaOther than that, maybe check that Surface doesn't store
all game saves, not just MS games, in your Cloud... also, have you asked about this on the Microsoft Community Support Forum - Gaming:
http://answers.microsoft.com/en-us/windows/forum/gaming?tab=ThreadsGood luck!