Can't log in as anything other than root

Question

Recently I installed Arch linux on my laptop.  Had a few problems with the install but I got there eventually.
I have installed gnome and lxde which I am using now with the log in manager that came with gnome.
Before I was using gnome/lxde I just logged in from the default login screen, and ran startx to load the x window manager and from there I would type startxfce4 to get into xfce.  All seems to go well on the root account, however, when I created a new user with
I added a new non-root user with useradd and all went well with no complaints.  I set up a password for it too.
When I logged out of root and tried to log in as my non-root user it said something like
"timed out locking in authority file" - not sure the exact words.
one time it loaded x window manager (but could not load xfce4) but since then it has loaded a black screen with nothing on it.  After installing gnome and lxde and using the gnome login manager, my new user shows up on the login menu, however, when trying to log in to lxde it loads into the DE but a popup says: "Error:  Invalid Directory" (or something like that).  No applications are in the menu and all other buttons are unresponsive, had to reboot.
I Can not log in to any usable DE at this stage.  I can only successfully log into non-root accounts using the default arch login screen (which i no longer am using). 
I do have access to a live version of arch.
I really want to get this fixed as not only is it bad practice to run under root all the time, but many applications won't run as root.
Any help would be much appreciated, but I'm new to this so you're probably going to have to be quite detailed; I came from Linux Mint 12 which kinda did everything for me.

Answer 1

lsblk:
sda      8:0    0 232.9G  0 disk
├─sda1   8:1    0     8G  0 part /
├─sda2   8:2    0    53G  0 part
├─sda3   8:3    0     1K  0 part
├─sda4   8:4    0  72.2G  0 part /home
├─sda5   8:5    0  95.7G  0 part
└─sda6   8:6    0     2G  0 part
sdb      8:16   1   3.7G  0 disk
└─sdb1   8:17   1   3.7G  0 part /run/media/root/PENDRIVE
mount
proc on /proc type proc (rw,nosuid,nodev,noexec,relatime)
sys on /sys type sysfs (rw,nosuid,nodev,noexec,relatime)
dev on /dev type devtmpfs (rw,nosuid,relatime,size=1027104k,nr_inodes=219199,mode=755)
run on /run type tmpfs (rw,nosuid,nodev,relatime,mode=755)
/dev/sda1 on / type ext4 (rw,relatime,data=ordered)
securityfs on /sys/kernel/security type securityfs (rw,nosuid,nodev,noexec,relatime)
tmpfs on /dev/shm type tmpfs (rw,nosuid,nodev)
devpts on /dev/pts type devpts (rw,nosuid,noexec,relatime,gid=5,mode=620,ptmxmode=000)
tmpfs on /sys/fs/cgroup type tmpfs (rw,nosuid,nodev,noexec,mode=755)
cgroup on /sys/fs/cgroup/systemd type cgroup (rw,nosuid,nodev,noexec,relatime,xattr,release_agent=/usr/lib/systemd/systemd-cgroups-agent,name=systemd)
pstore on /sys/fs/pstore type pstore (rw,nosuid,nodev,noexec,relatime)
cgroup on /sys/fs/cgroup/cpuset type cgroup (rw,nosuid,nodev,noexec,relatime,cpuset)
cgroup on /sys/fs/cgroup/cpu,cpuacct type cgroup (rw,nosuid,nodev,noexec,relatime,cpuacct,cpu)
cgroup on /sys/fs/cgroup/memory type cgroup (rw,nosuid,nodev,noexec,relatime,memory)
cgroup on /sys/fs/cgroup/devices type cgroup (rw,nosuid,nodev,noexec,relatime,devices)
cgroup on /sys/fs/cgroup/freezer type cgroup (rw,nosuid,nodev,noexec,relatime,freezer)
cgroup on /sys/fs/cgroup/net_cls type cgroup (rw,nosuid,nodev,noexec,relatime,net_cls)
cgroup on /sys/fs/cgroup/blkio type cgroup (rw,nosuid,nodev,noexec,relatime,blkio)
systemd-1 on /proc/sys/fs/binfmt_misc type autofs (rw,relatime,fd=35,pgrp=1,timeout=300,minproto=5,maxproto=5,direct)
configfs on /sys/kernel/config type configfs (rw,relatime)
hugetlbfs on /dev/hugepages type hugetlbfs (rw,relatime)
mqueue on /dev/mqueue type mqueue (rw,relatime)
debugfs on /sys/kernel/debug type debugfs (rw,relatime)
tmpfs on /tmp type tmpfs (rw)
binfmt_misc on /proc/sys/fs/binfmt_misc type binfmt_misc (rw,relatime)
/dev/sda4 on /home type vfat (rw,relatime,fmask=0022,dmask=0022,codepage=437,iocharset=iso8859-1,shortname=mixed,errors=remount-ro)
gvfsd-fuse on /run/user/0/gvfs type fuse.gvfsd-fuse (rw,nosuid,nodev,relatime,user_id=0,group_id=0)
fusectl on /sys/fs/fuse/connections type fusectl (rw,relatime)
/dev/sdb1 on /run/media/root/PENDRIVE type vfat (rw,nosuid,nodev,relatime,fmask=0022,dmask=0077,codepage=437,iocharset=iso8859-1,shortname=mixed,showexec,utf8,flush,errors=remount-ro,uhelper=udisks2)
df -h:
Filesystem      Size  Used Avail Use% Mounted on
/dev/sda1       7.8G  5.5G  2.0G  74% /
dev            1004M     0 1004M   0% /dev
run            1005M  736K 1005M   1% /run
tmpfs          1005M   84K 1005M   1% /dev/shm
tmpfs          1005M     0 1005M   0% /sys/fs/cgroup
tmpfs          1005M   12K 1005M   1% /tmp
/dev/sda4        73G  530M   72G   1% /home
/dev/sdb1       3.8G  529M  3.2G  14% /run/media/root/PENDRIVE