New Airport Extreme Setup: Accessing the HDD

Have you tried going into the settings of the Linksys router and turning off the hardware firewall? That could be blocking access to the hard drive from the Internet.

You could research the devices port that use remote access and compare that to the ports (that you need to open on the Linksys ports) to the "Well Known" TCP and UDP Ports By Apple software Products. However if you are not super tech savy I urge you use services like Slink or ShareTool (as well as others that could do the same) and use one of those remoter services.

Other posters interpret "connect outside the network" as meaning that you'd like to get into your network and at the drive from outside -- from another location.

But I'm wondering if you don't mean "get outside," that is, connect to the internet.

If the Linksys is doing the routing (meaning, acting as the DHCP server and NAT) have you set the AE to "bridge" mode, so that it doesn't try to be a router/NAT itself?

When I made some changes to my Time-Warner account, they brought me a Ubee modem/router combo which (until I figured out how to place the Ubee into bridge mode) insisted on being the NAT and DHCP server, and the only way I could make my Time Capsule work was to switch it into bridge mode.

You say that it's not your choice, but does this mean you can't get rid of the Linksys?

Or can you at least temporarily take it out of the chain and go directly modem-->AE? If that works, then you know where the problem lies.