Well there is a device transfer wizard in Desktop Manager 4.3 which I believe will back up/restore applications installed wirelessly. So try doing what caneau said and charge the battery in your new one, but that battery in your old one, use Bluetooth to pair it to your computer and to Desktop Manager, then run the device transfer wizard and I am pretty sure that will transfer your applications. I tried doing it from an 8830 to a Pearl and while it did transfer the applications, they didn't work because it's a totally different device. But since they're the same it should work.
Good luck man