Networking support for Layer 3 routing between 2 networks.

We have 2 datacentres which are connected via a private link that have been configured to talk to each other and appear to work in some ways, but the full routing of all devices is not work. We therefore need support from someone who understands network and can guide us through configuration. Remote access to the network WILL NOT be provided, but I can answer any and all questions and perhaps screen share.

What we have working;

Switches can ping each other on local and stub IP addresses
Switches can ping remote gateway at remote end.

What does not work;
Pinging any other remote device at remote end
Pinging any remote device from any local device

So we need to work the issues above through.

There are no routers, we have an L3 switch at each end and if appicable, a cisco ASA as the default gateway. There are multiple networks/vlans at main site and a single network/vlan at remote site.

Thanks