You took a good first step by testing everything while directly connected.
Since it works while connected via Ethernet, that proves your basic networking IP/netmasks are set correctly.
Your second step failed showing that just your wireless settings between the WRT and DAP are not compatible.
So compare the purely wireless settings between the boxes.
- 2.4 vs 5 Gz
- SSID (539)
- Security (none)
- etc.