Can you ping anything from your work network. It is not uncommon for traffic to be filtered from a company network since it is good security practice. Most companies even filter the web traffic for content.
It would be common to allow you to be able to ping machine that were inside your company network but not those outside. Really the only way you are going to find the answer is to get into the router/firewall going to the internet and see if there are restrictions configured.
It could also be the firewall settings on the PC itself. If it get into the wrong type of network it will restrict certain types of traffic.
Some websites disable ICMP replies to avoid having problem with DDoS attacks.
That's absolutely right.
OP, why do you need to be able to ping Google from your work computer? I'm a Network Administrator and disabling ICMP requests outside the LAN is very common. The most likely reason why it works within the LAN is for troubleshooting purposes, so your IT team can establish the quality of your computer's network connection.