If your other domain gives you access to the webserver logs then you may see something under the error.log.
It could be that the other domain/web host is set up to not allow wget to access cgi from outside the domain.
Are you familiar with using SSH to access your DreamHost shell? You could try running the wget program from the command line and you should see any errors.
Also try using lynx in place of wget and see how that fairs.
/usr/bin/lynx http://www.mydomain.com/dellogs.cgi > /home/username/example.com/errors.txt 2>&1
Which should send any errors to/result to errors.txt where you can view it.
Likewise under cron you could try wget again to see the output.
* * * * * /usr/bin/wget http://www.mydomain.com/dellogs.cgi > /home/username/example.com/errors.txt 2>&1
Then when it is working you can replace error.txt with /dev/null
Opinions are my own views, not DreamHosts'.
I am NOT a DreamHost employee OK! :@
Act on my advice at your own risk!