Hi MrsJH,
Well, not sure what information you are concerned with losing. Your iCloud backup is there in case you need to restore your device or set up a new device using that backup. The information on the device itself won't go anywhere even if you delete your backup.
However, deleting your backup will not help with storage issues on your actual phone. If you are running out of room on your phone, then you need to to to Settings>General>Usage>Manage Storage, and see what is taking up so much room.
For example, if your Photos are taking up a lot of space (mine take up about 11 GB), then you are going to want to back them up to an external source. If you cannot import them to your computer, then download an app like Dropbox so that you can upload your photos to that Cloud service, and then delete them from your phone (once you have verified that they are in Dropbox).
You may also want to delete some apps that are taking up a lot of room. In addition, any Messages or emails that you have that have videos attached to them will take up a lot of room - delete those.
Not sure if you have already gone through this troubleshooting article for iOS device not recognized, but it might help:
iOS: Device not recognized in iTunes for Windows
If you are able to get your device recognized by your computer at all, you may want to try to import your photos to your Photo Library on your computer:
IMPORTING PHOTOS - WINDOWS/MAC
Post back with any questions!
Cheers,
GB