DNS might be an issue, but it's unlikely. There's a deeper problem here.
If you're pinging by IP address, which I assume you are, DNS queries don't result in failed pings. You're going to want to check your route table to make sure that your computer knows where to send things. Here's an example of what this should look like:
Kernel IP routing table
Destination Gateway Genmask Flags Metric Ref Use Iface
172.31.0.0 * 255.255.0.0 U 0 0 0 eth0
default 172.31.1.250 0.0.0.0 UG 0 0 0 eth0
There are two entries here that allow my machine to communicate with the rest of the network. The top most entry allows my communication with the local network, while the bottom entry is my default route to access the outside world.
I have seen issues on certain versions of Linux when using the lightweight DHCP servers on routers where the route table entries are not made correctly in certain situations.
As per bejiita's suggestion to check DNS, you'll want to do this too. There's a strong possibility that this wasn't pulled correctly from DHCP as well.
Let us know how things turn out!