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Is it saying specifically that your "Text Memory" is full?
Ok, this should work, but if not, it at least narrows down the issue for me and tells me what it is (which we do not want it to be).
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Ok, then what that tells me is that the data is corrupt and you are not able to clear it, and its stuck at a system level and the system thinks its full. The only way to fix that, is with a reset... but its not as bad as it sounds.
As long as you have a Google account synced to your device, your contacts, calendar, etc. will be re-synced to the device after you run the initial setup again as long as you sign in with the same Google/Gmail account. Any apps you have paid for, you can get back after you reset the device by opening the Market, pressing Menu on the phone and choosing "My Apps".
I recommend you go to http://google.com/contacts on your computer(with the same google account thats on the phone) then check all your contact groups to make sure the contacts are synced(if not, ask me about contact backup instructions).
As far as any data that is stored on the SD Card(images, music, etc.), it will not be erased. Only the phones internal memory is formatted.
If you need to know how to reset the phone, just let me know.
Can you tell me the make and model? This way, I can give you the true reset method.
Ok, for that one our only option is going through the settings. Open the Settings App, choose Privacy, then choose Factory Data Reset. You will want to press OK if it asks you to confirm deleting all data.
As I mentioned, if you sign back in with the same Google Account, anything that was synced will be resynced. You can get your apps back (paid) from the Market without paying again also. And, if you needed help backing up contacts, after you check google.com/contacts as I mentioned, I will tell you how to do it.
Is it still giving you this error?