Thanks for all the replies. I was trying both Firefox and Chrome on my Windows 7 PC as well as Safari (along with Firefox and Chrome) on my Mac. Also tried Safari on my iPhone (also using dish.com). Might be an issue that both my computers and iPhone are old, but the web browsers are up to date.
Thanks "ClarkGable" for your advice as I was mainly trying the "Log in to myDISH" link at the top left of dish.com that I normally use. I tried the "myDISH" link under the "DISH sites" heading again since you suggested it, and with much patience myDISH.com eventually loaded and I was able to log in.
I called DISH Tech Support today and apparently several customers are experiencing the same log in difficulties through the dish.com website (rather than the app). I guess they are working on a fix. Not sure why it works for some and not others, but again it might be that both my computers and iPhone are ancient.
Thanks again.