HTC Desire :: No Space Left On Device

While on holiday my HTC Desire starting reporting that it was running out of space. It could never figure exactly what was taking up the space unfortunately, but I assume one of my apps was using a stupid amount of data.

Anyway on the last day of my holiday the phone refused to boot at all. It shows the HTC screen, then the carriers custom splash screen (T-Mobile), then reboots and goes back to the HTC screen in an endless loop.

I booted the device into the recovery console and received the following errors:

E:Can't open /cache/recovery/command
E:Error in DATA:data/recovery/log
(No Space left on device)

I'm aware that I could do a factory reset, but I don't really want to lose all of my apps, scenes and other data if I can possibly help it.

I found one site where a guy claimed to have been able to fix the problem by connecting to the device using adb and then deleting some files, but I can't get adb to recognise the phone. 'adb devices' always returns nothing.

So, can anyone tell me how to get my phone (which won't boot into anything other than fastboot and recovery) to connect to adb so I can wipe some files? Will the phone have to be rooted to do this? (It isn't).

Do I have any other options other than a factory reset?