Image loading issue

Pardon me if this question has an easy answer, but I am absolutely new to WordPress. Here are the symptoms.

When I put in the URL of an image (after checking the URL in a browser window to make sure it’s good), after I publish post the image comes up with the missing/broken image symbol instead of the image. This is using the same browser I tested the link in (Firefox, not that it would be acceptable for this to happen no matter what browser I was using.)

So, I tried using the built-in WordPress function for placing images in posts and the same thing happened. THEN, I tried using the upload function and found that this function seemed to lack fine control over placement and was too clunky for uploading, say, 14 images when I could simply make a table quickly using a tool offline, creating images with very similar filenames (e.g., image01.jpg, image02.jpg, etc.) and really whip a table together.

First off, what is wrong with WordPress that it gives me a broken image when I give it a good, tested link?

Is there some reason I should even need to use that? I know how to write HTML and creating a table with images should be a snap if WordPress doesn’t “burp” when I try to insert it in the writing box.

Any solutions coming to mind? I searched but couldn’t find anyone who seemed to to be having quite the same problem.