We'd need to see a topology diagram to be sure, but if your SH is in modem mode and connected to a switch as described then you've probably either cross patched both your internal and external networks or don't have anything doing and routing/NAT to/from your ISP, or put your NAS outside the firewall of the AIrport (ie direct on the Internet) any of which which will cause you all sorts of pain.
Routers are used to join separate networks together. In a SOHO router the networks are A) everything participating in your internal network (downstream of the LAN ports and wi-fi connected devices) and B) everything upstream of the WAN/Internet port of your ISP connected router. Connected and configured as you've described you've possibly cross-patched your internal and external networks and eliminated the separation of the two.
Either:
Turn off modem mode in your SH and use it as a router and leave connected as described then use the Airport solely as a Wi-Fi Access Point (as described in this forums "Using two routers together" FAQ.) You'll need to refresh all the IP addresses of your client devices if you do this.
Or:
If you're determined to use the airport as a router, connect SH (modem mode) direct to the WAN/Internet port of the Airport (with nothing in between) and connect your switch downstream of one of the Airport LAN ports.