Are you sure that the problem is with Picasa, and not with your card reader? Try this to check:
Double-click on the drive icon which represents your card reader (or the relevant slot in your card reader). If necessary, double-click on folders until you can see the icons (or thumbnails) which represent your picture files. If you can get this far, there's probably nothing wrong with your card reader. (If you can't see the files, your card reader may be faulty). For a final check, right-click on any of the files, select 'Open with' and choose any suitable program other than Picasa.
Assuming that you're card reader is OK, then reinstalling Picasa seems to be a sensible idea. Picasa only accesses your picture files; it doesn't hold them within the program itself, so reinstalling shouldn't affect your existing files.
If you're still in doubt, you can easily back up your picture files by copying them to another location on your PC, or by storing them on removable media, such as a CD or pen drive. Assuming that you've saved your files in the usual jpeg format, you can quickly locate them by searching for *.jpg
Chris