According to the logs, your display is managed by the basic "vesa" driver,
not the "radeon" one:
[ 19.222] (II) Loading /usr/lib/xorg/modules/drivers/radeon_drv.so
[ 19.223] (II) [KMS] drm report modesetting isn't supported.
[ 19.223] (II) GPU only supported with KMS, using vesa instead.
[ 19.223] (II) Loading /usr/lib/xorg/modules/drivers/vesa_drv.so
"GPU only supported with KMS" means "Graphics Processing Unit only supported
with Kernel Mode-Setting". So, yes, the problem is at the kernel level (or do
I misunderstand that laconic English?) and your only hope is to update it.
Have you really installed the 3.11 version as I suggested you? The 'uname -r'
command (to be entered in a terminal) will tell.
If so, you can only hope that the very latest 3.13 better supports your card.
Here is the documentation (the section "Using jxself's repository") to do
that update: https://trisquel.info/en/wiki/update-linux-libre-kernel
Notice the use of 'gksu' (or 'gksudo', they are aliases) before the call of
the text processor ('gedit' is used in the documentation) so that it can edit
system files. That is the solution to the trouble you faced when being denied
permissions.
