Hey there,
Yep, having your root filesystem 100% full would bring down whatever is running there.
What part of the guide you linked to didn't work for you? (What is the output you see during / after you run the commands listed there?) Note that you must resize the partition using:
sudo growpart /dev/[DEVICE_ID] [PARTITION_NUMBER]
before you resize the filesystem itself:
sudo resize2fs /dev/[DEVICE_ID][PARTITION_NUMBER]
If you don't do that, resize2fs will not be able to grow past the end of the partition to use up the newly added space.
Thanks,
Dan