I am using a relative link within the HTML page to the image file. And, as suggested, I zipped up the two files into a folder, uploaded the zipped file to Moodle (by adding a Resource ... File) and unzipped it in Moodle. I then made the HTML file the 'main file'. Still the link does not work. As I mentioned in my first post, I have had no problem with exactly the same files, adding them as a Resource-File in a Moodle 2.1.1+ install and a Moodle 2.3.2 install. The image works perfectly.
However, one big difference, other than the version of Moodle, is that the Moodle 2.2.6 install is on a GoDaddy Host. I initially had a difficult time on this install even getting files to display, as I was receiving a 'No input file specified' error message. To solve that problem I had to go to Admininstration > Server > HTTP and change the 'Use slash arguments' to no (from the default of Yes). If as you, suggest this should work pretty much the same in Moodel 2.2.6 as it does in Moodle 2.1 and Moodle 2.3, then I am definitely thinking that this again must be a server issue. Is there any other place that I should look?
Thanks for your suggestions,