Start-up disk is full and can't go past the blue screen; can't delete read-only files on single-user mode. Please help.

I have had my Mac mini for about 6 years and I guess it had enough of me (haha), so the start-up disk got full and it shut down before I could empty files on my drive. Unfortunately, all these years I hadn't backed up anything and now I can't access anything since it won't boot past the apple logo (and the blue screen for that matter). I have tried rebooting (holding shift as the mac mini loads), but that didn't help since the start-up disk will still be full and stuck on the blue screen. I am now trying the single-user mode (holding command key+s), and I tried to delete files in the trash bin but all of the files are read-only and access is denied! so I basically can't delete anything on the mac mini (it says "Root device is mounted read-only"). So the key here is to change the permissions but I don't know how to exactly do that. Can someone help me figure this out? (and type the command in the unix language please!!) [ Note: We have two users on this mac mini if that helps.]