Doing a reinstall shouldn’t have any impact on your existing databases or reports. The databases can be reattached, as can the reporting services databases. When the new reporting services instance checks in it should pick up all the reports.
Before doing the reinstall be sure to export all the encryption data from the SSRS configuration tool.
All your historical job data will be replaced by the new MSDB database.
Try reinstalling the service pack or hotfix that you are running. This may reregister all the DLLs.