No connections work after starting OpenVPN service?

Question

I setup my Scientific Linux 6.2 as an OpenVPN client via the instructions here, and restarted my OpenVPN service. I checked /var/log/messages and it says the VPN connection was established. However, now I cannot make any connections out of my computer! Browsing with Firefox gives me "Server not found" errors, and even ping and traceroute don't work (they produce unknown host errors).

How can I troubleshoot this issue? BTW, is there a way to route only certain traffic through this VPN (once I get it working), while everything else don't?

Thanks!

My OpenVPN /etc/openvpn/client.conf looks like this:

<connection> 
remote [VPN host here] 1194 udp 
</connection> 
<connection> 
remote [VPN host here] 1195 udp 
</connection> 
auth-user-pass 
client 
ca ca.crt 
cert client.crt 
key client.key 
dev tun 
topology subnet 
ns-cert-type server 
nobind 
persist-key 
persist-tun 
reneg-sec 72000 
ping 5 
ping-restart 20 
ping-timer-rem 
tls-client 
pull 
comp-lzo 
verb 2

And here is my ifconfig output after OpenVPN service starts:

eth0      Link encap:Ethernet  HWaddr 08:00:27:85:0B:E5  
          inet addr:10.0.2.15  Bcast:10.0.2.255  Mask:255.255.255.0
          inet6 addr: fe80::a00:27ff:fe85:be5/64 Scope:Link
          UP BROADCAST RUNNING MULTICAST  MTU:1500  Metric:1
          RX packets:181793 errors:0 dropped:0 overruns:0 frame:0
          TX packets:42981 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:1000 
          RX bytes:174493756 (166.4 MiB)  TX bytes:2766010 (2.6 MiB)

eth1      Link encap:Ethernet  HWaddr 08:00:27:71:4E:F5  
          inet addr:192.168.56.111  Bcast:192.168.56.255  Mask:255.255.255.0
          inet6 addr: fe80::a00:27ff:fe71:4ef5/64 Scope:Link
          UP BROADCAST RUNNING MULTICAST  MTU:1500  Metric:1
          RX packets:2905 errors:0 dropped:0 overruns:0 frame:0
          TX packets:1890 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:1000 
          RX bytes:332246 (324.4 KiB)  TX bytes:487561 (476.1 KiB)

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:16 errors:0 dropped:0 overruns:0 frame:0
          TX packets:16 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:0 
          RX bytes:1412 (1.3 KiB)  TX bytes:1412 (1.3 KiB)

tun0      Link encap:UNSPEC  HWaddr 00-00-00-00-00-00-00-00-00-00-00-00-00-00-00-00  
          inet addr:10.1.3.33  P-t-P:10.1.3.33  Mask:255.255.255.0
          UP POINTOPOINT RUNNING NOARP MULTICAST  MTU:1500  Metric:1
          RX packets:314 errors:0 dropped:0 overruns:0 frame:0
          TX packets:384 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:100 
          RX bytes:38675 (37.7 KiB)  TX bytes:46675 (45.5 KiB)

This is the result from "ip route show":

10.0.2.0/24 dev eth0  proto kernel  scope link  src 10.0.2.15 
192.168.56.0/24 dev eth1  proto kernel  scope link  src 192.168.56.111 
169.254.0.0/16 dev eth0  scope link  metric 1002 
169.254.0.0/16 dev eth1  scope link  metric 1003 
default via 10.0.2.2 dev eth0  proto static