No internet via ethernet to iMac

From the iMac's Wi-Fi menu, select Open Network Preferences...

If it does not resemble this, describe what's different.

Is there a reason you are using a static IP address?

If not, or you don't know what that means, change your settings to resemble the screenshot I posted: Configure IPv4 "Using DHCP". Then, click the Apply button. The other fields will be supplied by your AirPort Extreme, though the numbers will probably be different.

If it still does not connect, cycle the power on your Extreme. Unplug it from the wall, wait a moment, then plug it back in.

If you decide those changes made things worse, return to the previous settings.

The speed is likely being limited by your ISP as you suspect, but 15 Mbps should be sufficient for the highest resolution video available at present. Just keep in mind that 15 Mbps is shared among all your devices, so if you're streaming movies on your AppleTV you'll want to make sure nothing else is doing anything particularly demanding.

To test the AppleTV's connection speed. Apple recommends using "an online bandwidth test on a computer on the same network as your Apple TV."

All else being equal, the length of the Ethernet cable should not affect transmission speed. The maximum permissible length is 100m.

I am concerned about the speed differences you describe when comparing one Ethernet link to another. They should be identical, on average. If there is a difference in performance between two cables, one of them is likely to be damaged, not completely intact, or not properly rated. Cables are inexpensive enough to substitute one for another, to determine if the difference can be explained by a defective cable.

On the other hand wireless transmission speeds can vary tremendously, depending on a variety of often unpredictable factors, which is the reason to always use a wired network connection whenever practicable, especially for an AppleTV. A wired connection's transmission speed should be consistent. Measuring the length of time to load a large file as you describe is as good a method as any.

It is also possible that a parameter in the AirPort Extreme may have become corrupted, in which case a "hard reset" followed by reconfiguring the Extreme is justified. Sometimes that is the only way to resolve otherwise inexplicable performance problems.

In any event your ISP's 15 Mbps speed should be more than adequate, and movie trailers ought not to load objectionably slowly. Confirm that you are actually realizing that speed by substituting your MacBook Pro at each connection point - the iMac's connection as well as the AppleTV's connection separately - and running the bandwidth test at each point. You should see identical results. Significant differences that cannot be explained by transient Internet conditions beyond your home's network (in other words, beyond your control) require investigation.

The difference in loading time is not comparing different cables, but comparing WiFi to Ethernet. Do you think these should both have to same speed?

No, not at all. I would expect the same results only under ideal wireless conditions, which are rarely found anyplace other than in sparsely populated areas. Wi-Fi speed will never exceed whatever wired throughput you can achieve, is generally much slower, and can be very inconsistent.

If someone else was using the computer while I tested it, is that likely to be slowing it down?

If other users on your network - including the computer you're using - are performing any network-related activity at all, they will have an affect on network throughput, wired or wireless. The degree to which it will slow overall network throughput is a function of just what network activity is taking place.

This is what concerned me:

Then when I just had the iMac to Airport connected via Ethernet, it took roughly 8.

And fully over Ethernet was only 4.

Quite a big difference.

You clarified that in your subsequent reply:

The difference in loading time is not comparing different cables, but comparing WiFi to Ethernet.

If you are not experiencing any significant differences from one Ethernet connection to another, then there is no concern.