I tried clearing the cache, but I don't even have a Stardock folder in the path described in the tutorial (Documents and Settings->Application Data
That would be because you installed OD via the e-mail link you received. By installing via SDC you will have a cache folder

I did the same as you...had installed via the e-mail link....chose to uninstall & install via SDC...allows a cache that may well be causing your problems...When you have been changing settings or images ect ...a build up saved files can cause problems....not a technical explanation by any means but gets to the meat of the issue
The same thing when you have been installing & reinstalling programs...registry changes occur and left over entries can cause issues with new program installs. It is a good practice to clean the registry each time you uninstall
any program.

I have been doing this for years and do not have issues with programs.
Edit: can the SDC download manager be deleted completely after having installed OD through it?
SDC is not just a download manager...it allows you to completely & cleanly uninstall any Stardock programs. You will need SDC to uninstall OD if you installed it that way. As well as allowing easy access to the Galleries & the website. It also allows you to easily know when any updates are available on any of the purchased software.
SDC has many settings available that make keeping updated easy & secure. You will also find under setting the option to show pre-release or beta versions of programs...there is a major beta of OD right now that I am using and there are major improvements and awesome additions to the program. SDC uses no resources unless you choose to keep the setting found under auto update...to check every hour for updates. Otherwise the program uses nothing until you open it. Go to tools then settings to change this.
And finally yes it can be completely uninstalled but I have yet to find a reason to do so.

And would not have had the pleasure of using the newest OD beta right now if I had.
And this is a link to a post about the improvements to OD in the 1.6 beta 1.59b
HEREIt's My Secret