You say they wont open, what type of files are they?
If, for example, they are Microsoft Office files and you have not got Office installed then they wont open.
Are you sure you actually copied the FILES to the memory stick. If so then they should open (if you have the software installed) no problem from a memory stick.
HOW did you copy them to the memory stick. There is a possibility (if you did not do it right) you only copied a SHORTCUT to the file and not the file itself.
Spend a bit of time looking at the files on the memory stick and see if you can find out if they are actually there, if they have a SIZE of file given for example.
Normally copying files to a memory stick (if you did it right) should not be a problem so not sure what you did wrong.
btw It is probably worth getting an external hard drive and copy your files to there on a regular basis, That way if you do get a virus or other problem you know you always have a backup.