I'm not sure if this will help or not... The GOTD is over but you might still have Reg Organizer installed & just need to get it working. Otherwise some parts of this post might hopefully be useful if anyone encounters this sort of problem in the future, with a GOTD or any other app.
Using Process Explorer, Reg Organizer seems to have very few dependencies [stuff that you need to have in place for it to run]. It uses Internet Explorer, but if you didn't have that working I wouldn't think you would have been able to install the GOTD -- there are many posts, it's in the FAQ I think etc. that Internet Explorer has to be installed & set to work on-line for the GOTD installer to call home, verify the date, & run the app's setup program... but they've updated the GOTD installer recently so I could be wrong, so maybe make sure Internet Explorer is working.
Again using Process Explorer, Reg Organizer uses Windows XML [e.g. msxml3r.dll], a file named gdi32.dll, the Microsoft C Runtime [in my case msvcr90.dll], & maybe Direct Show for some window animation. Normally none of that's any big deal, but I've seen misbehaving software [not Reg Organizer in this case] screw up 1 of those four on rare occasions -- if/when that happened some other software [besides Reg Organizer] wouldn't run properly either.
Depending on how much you want Reg Organizer working, & just FWIW, if/when an app won't work like this I'll check Task Mgr. to see if the app's running & just not showing the program's window. Then I'd use Google/Bing, check the app's forums if available, & contact the developer if or as possible in case it's happened to someone else & been cured. If not, & if the app runs but won't display, I'd use Process Explorer [from Sysinternals at microsoft.com] to see if I can detect the problem -- several times I've right clicked on a misbehaving app in Process Explorer, selected Properties, & then gone to the Threads tab in the pop-up window, where I've seen one file appearing/disappearing quite often [you *might* have to select the app's .exe file & click the Stack button if nothing's apparent in the regular view], & that file was the source of the problem. It might be an unneeded file that I could rename to turn it off, it might be corrupt or it might be the wrong version etc. where replacing it fixed the problem.
If the app in question doesn't seem to be running at all when I check Task Mgr. & try starting the program, I 1st check to see if it's all there, if it completely installed. If Universal Extractor or 7Zip works to expand everything in the setup file that's one way to get an idea of what should be installed -- for the Reg Organizer GOTD you can't expand the GOTD setup.exe because it's encrypted, but you can expand the trial download setup program. It's more accurate to monitor the install in a VM [Virtual Machine], on another PC/laptop, or after booting into another copy/version of Windows [assuming it works in those alternatives], because that way you can track or record everything going on in the registry as well, but I don't think most people have that sort of thing available. In this case monitoring the install I found that Reg Organizer doesn't seem to use/need any critical registry entries, but I could check [search in Regedit] for the main key: "ChemTable Software" [no quotes] -- if it's not there it isn't getting written to the registry [I then have to figure out why], & if it is there I could try deleting it before a reinstall [in case there's some wrong value]. I'll next check the logs for my AV [Anti-Virus or anti-malware] software to see if it did anything to stop the app from working.
Once I'm pretty sure everything's there, as above I'll use Google/Bing, check the forums, try to contact the developer etc.
If all else fails Process Monitor [also Sysinternals] will usually help... it logs very near Everything going on with Windows internally. What you do is find out when in the chain of events the app broke or quit, e.g. was it looking for a file or registry entry & couldn't find it, had it just loaded a file etc. Once you find out where & when it's breaking you figure out why. The hard part that makes it a last resort for me is that there's an awful lot of events to wade through looking for the one(s) you want -- I turn off everything non-essential, like my Logitech mouse/keyboard app to reduce the number of entries, I save the log because while I'm looking at all those entries the list will continue to grow, & I use Process Monitor's built-in tools to try & filter what I see, so I don't have to look through so many entries.