said by doulos2k:
There is a system within the client network that we have been given access to and we need to be able to direct connect to that machine. They've opened up the IPs to ensure we can ping from our network to theirs, but I'm unable to access that machine. They don't see attempts on their side, so I've come to the conclusion that there must be something preventing it on my side.
I recalled when I was in your position managing a cloud network for customers, we had similar situation. It turned out that the customer had some NAT device that hid the customer's actual IP address. When that is your case, then the customer needs to create either some static NAT to an IP address accessible to your network, or disable NAT at least for such machine.