OpenVPN not routing over tun0 interface

I've looked at a lot of different pages on this site and in other places but I couldn't find any solution to this problem I've spent the afternoon on.

I want to setup an OpenVPN server on a VPS CentOS 6.5 machine. I have successfully done that and I'm able to establish a tunnel to the server, ping the remote gateway IP address etc. However I am unable to reach Internet from the VPN. After a lot of time troubleshooting the OpenVPN configuration, I believe the issue comes from the VPS itself since the tun0 interface itself can't reach Internet (so it can't very well route it!).

If I try to reach Internet from the tun0 (OpenVPN) interface, it doesn't work:

[root@vps3580 ~]# ping -I tun0 8.8.8.8
PING 8.8.8.8 (8.8.8.8) from 10.44.3.1 tun0: 56(84) bytes of data.
--- 8.8.8.8 ping statistics ---
6 packets transmitted, 0 received, 100% packet loss, time 5301ms

If I ping from the default interface (venet0:0) it works fine:

[root@vps3580 ~]# ping -I venet0:0 8.8.8.8
Warning: cannot bind to specified iface, falling back: No such device
PING 8.8.8.8 (8.8.8.8) from 37.187.42.146 venet0:0: 56(84) bytes of data.
64 bytes from 8.8.8.8: icmp_seq=1 ttl=49 time=10.0 ms
64 bytes from 8.8.8.8: icmp_seq=2 ttl=49 time=10.0 ms
--- 8.8.8.8 ping statistics ---
2 packets transmitted, 2 received, 0% packet loss, time 1793ms
rtt min/avg/max/mdev = 10.038/10.056/10.074/0.018 ms

This is what my ifconfig looks like (I modified the public IP for this post) :

[root@vps3580 ~]# ifconfig
lo        Link encap:Local Loopback
          inet addr:127.0.0.1  Mask:255.0.0.0
          inet6 addr: ::1/128 Scope:Host
          UP LOOPBACK RUNNING  MTU:16436  Metric:1
          RX packets:5013190 errors:0 dropped:0 overruns:0 frame:0
          TX packets:5013190 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:0
          RX bytes:677461812 (646.0 MiB)  TX bytes:677461812 (646.0 MiB)

tun0      Link encap:UNSPEC  HWaddr 00-00-00-00-00-00-00-00-00-00-00-00-00-00-00-00
          inet addr:10.44.3.1  P-t-P:10.44.3.2  Mask:255.255.255.255
          UP POINTOPOINT RUNNING NOARP MULTICAST  MTU:1500  Metric:1
          RX packets:2004 errors:0 dropped:0 overruns:0 frame:0
          TX packets:1287 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:100
          RX bytes:223030 (217.8 KiB)  TX bytes:329848 (322.1 KiB)

venet0    Link encap:UNSPEC  HWaddr 00-00-00-00-00-00-00-00-00-00-00-00-00-00-00-00
          inet addr:127.0.0.1  P-t-P:127.0.0.1  Bcast:0.0.0.0  Mask:255.255.255.255
          inet6 addr: 2001:41d0:52:100::e84/56 Scope:Global
          UP BROADCAST POINTOPOINT RUNNING NOARP  MTU:1500  Metric:1
          RX packets:1027193 errors:0 dropped:0 overruns:0 frame:0
          TX packets:878383 errors:0 dropped:318 overruns:0 carrier:0
          collisions:0 txqueuelen:0
          RX bytes:508829024 (485.2 MiB)  TX bytes:133008265 (126.8 MiB)

venet0:0  Link encap:UNSPEC  HWaddr 00-00-00-00-00-00-00-00-00-00-00-00-00-00-00-00
          inet addr:73.83.42.22  P-t-P:73.83.42.22  Bcast:37.187.43.255  Mask:255.255.252.0
          UP BROADCAST POINTOPOINT RUNNING NOARP  MTU:1500  Metric:1

And my routes:

[root@vps3580~]# route
Kernel IP routing table
Destination     Gateway         Genmask         Flags Metric Ref    Use Iface
10.44.3.2       *               255.255.255.255 UH    0      0        0 tun0
10.44.3.0       10.44.3.2       255.255.255.248 UG    0      0        0 tun0
73.83.42.22     *               255.255.252.0   U     0      0        0 venet0
link-local      *               255.255.0.0     U     0      0        0 *
link-local      *               255.255.0.0     U     1002   0        0 venet0
198.18.0.0      *               255.254.0.0     U     0      0        0 *
172.16.0.0      *               255.240.0.0     U     0      0        0 *
default         *               255.0.0.0       U     0      0        0 *
default         *               0.0.0.0         U     0      0        0 venet0

I suspect there is something wrong with one of the route but I can't figure out what. When I traceroute I get this:

[root@vps3580~]# traceroute -i tun0 8.8.8.8
traceroute to 8.8.8.8 (8.8.8.8), 30 hops max, 60 byte packets
 1  * * *
 2  * * *
 3  * * *
 4  * * *
 5  * * *
 6  * * *
 7  * * *
 8  * * *
 9  * * *
10  * * *
 [...]
30  * *

I'm not familiar with "tun" interfaces and I've been struggling with this for hours and was really hoping somebody could help me troubleshoot this!

Edit: Firewall rules:

[root@vps3580~]# iptables -S
-P INPUT ACCEPT
-P FORWARD ACCEPT
-P OUTPUT ACCEPT
-A INPUT -m state --state RELATED,ESTABLISHED -j ACCEPT
-A INPUT -p icmp -j ACCEPT
-A INPUT -i lo -j ACCEPT
-A INPUT -i venet0 -p tcp -m tcp --dport 80 -m state --state NEW -j ACCEPT
-A INPUT -i venet0 -p tcp -m tcp --dport 443 -m state --state NEW -j ACCEPT
-A INPUT -i venet0 -p tcp -m tcp --dport 22 -m state --state NEW -j ACCEPT
-A INPUT -i venet0 -p udp -m udp --dport 1194 -m state --state NEW -j ACCEPT
-A INPUT -j REJECT --reject-with icmp-host-prohibited
-A FORWARD -m state --state RELATED,ESTABLISHED -j ACCEPT
-A FORWARD -s 10.44.3.0/29 -j ACCEPT
-A FORWARD -j REJECT --reject-with icmp-host-prohibited