No, you can't delete the application without losing data. I recommend that you take a backup of the data you have and then delete it. Moreover, install any antivirus from the database of Software Informer and scan your system. Probably, the software you have installed works normally while other sub-components are actually infected preventing you from running it.
After the data is backed up and the computer is cleaned from virus infections, re-install the application and import the data.
