What are you doing for NAT (Network Address Translation)? If you let those 172.16.x.x addresses out onto the internet, they will not work (your ISP's routers will block them). Presumably you have setup, either in Checkpoint or somewhere else, the facility to route the 172.16.x.x addresses to the internet while translating their addresses a valid (134.x.x.x ?) address. NAT shuffles port numbers to keep track of who is talking to whom so that replies go back to the station which sent the originaltraffic.
The problem with NAT is that you cannot usually originate traffic from the internet to a NAT'ed station, since there is no way the outside station can address the inside station (clearly the 172.16.x.x address will NOT work). For servers, some NAT implementations allow you to specify that traffic for specific ports (e.g., 80 for http, 25 for smtp) go to specific internal addresses (your servers). Typically this will NOT be set up for ping. If NAT is set up correctly, this explains why the 134.x.x.7 address cannot ping the 172.16.x.x addresses. The fact that it can ping the NIC's on the router suggests that NAT is not set up properly.
Go over your Checkpoint setup. You should have an external network interface defined, which presumably is the 134.x.x.2. (Note that this means that ALL stations on that segment and beyond are the untrusted world.) Double-check your Checkpoint documentation to make sure that you can have two separate trusted networks. In the Checkpoint GUI,set up rules to permit all traffic between the 172.x.x.x segments, and allow whatever traffic you wish to and from the 134 segment, with NAT (if Checkpoint is providing NAT). If the Checkpoint is NOT providing the NAT, you must have a NAT router between the Checkpoint and the final internet router.
Good luck.
If the 134.x.x.x range is a range of addresses you are using internally, you need to
