Q:

Why I can't ping server on remote network from AWS through VPN

I've created a VPC in Amazon and created a number of subnets - both public and private. 
1 of these subnets is a private subnet that has a linux server in it. 
I've created a virtual private gateway for the private subnets and an internet gateway for the public subnets. 
I have created a customer gateway with the correct settings for the partner firewall and a VPN connection that uses that customer gateway. 
The other party has established a VPN tunnel to AWS and AWS reports the tunnel is up. 
They have pinged the server in the private subnet in AWS and can see it successfully. 
However I can't ping a server in their network from that same server in AWS.  
Their server is x.x.x.x (private ip on their network).  
My server ip is y.y.y.43 (private Ip in private subnet)

A traceroute from the server in aws to their server looks like this:
traceroute to x.x.x.x (private IP on their network), 30 hops max, 60 byte packets
1  * ec2-79-125-1-96.eu <http://ec2-79-125-1-96.eu> <http://ec2-79-125-1-96.eu> <http://ec2-79-125-1-96.eu>-west-1.compute.amazonaws.com <http://west-1.compute.amazonaws.com> <http://west-1.compute.amazonaws.com> (79.125.1.96)  2.494 ms ec2-79-125-1-102.eu <http://ec2-79-125-1-102.eu> <http://ec2-79-125-1-102.eu> <http://ec2-79-125-1-102.eu>-west-1.compute.amazonaws.com <http://west-1.compute.amazonaws.com> <http://west-1.compute.amazonaws.com> (79.125.1.102)  0.567 ms
2  178.236.0.138 (178.236.0.138)  1.390 ms 178.236.0.108 (178.236.0.108)  1.044 ms 176.32.106.132 (176.32.106.132)  0.625 ms
3  178.236.0.133 (178.236.0.133)  1.138 ms 178.236.0.117 (178.236.0.117)  7.105 ms 178.236.0.119 (178.236.0.119)  1.204 ms
4  213.242.106.85 (213.242.106.85)  1.319 ms ! N ae3.dub40.ip4.gtt.net <http://dub40.ip4.gtt.net> <http://dub40.ip4.gtt.net> <http://dub40.ip4.gtt.net> (141.136.96.137)  1.321 ms ! N 213.242.106.85 (213.242.106.85)  1.312 ms ! N

The VPC route tables looks like this:
destination y.y.0.0/16 target=local
destination x.x.x.0/24 target=virtual gateway
destination my-public-ip-I'm-connecting-from target=internet gateway

Routing table on server looks like this:
Kernel IP routing table
Destination     Gateway         Genmask         Flags Metric Ref    Use Iface
0.0.0.0         y.y.y.1     0.0.0.0         UG    0      0        0 eth0
0.0.0.0         y.y.y.1     0.0.0.0         UG    10001  0        0 eth1
y.y.y.0     0.0.0.0         255.255.255.0   U     0      0        0 eth0
y.y.y.0     0.0.0.0         255.255.255.0   U     0      0        0 eth1
169.254.169.254 0.0.0.0         255.255.255.255 UH    0      0        0 eth0

I have a security group associated with that server that allows ICMP and SSH incoming from my public IP I'm connecting to AWS from, outbound everything to everywhere. 
I have a network ACL associated with that server that allows ICMP and SSH incoming from my public IP, outbound everything to everywhere. 
How come I can't ping the server on their network?  How come the traceroute seems to be looking for public IPs? 

A:

So despite repeated requests to verify that ICMP was allowed on the other network, it appears that it wasn't.  Once they turned it on, everything worked.