TM template (some of them) DO overwrite core files...

So what can happen is that when you install another template, that relies on CORE functions, those functions may no longer be where the new template code is looking for them. So it gives up and stubbornly presents you with a blank screen.

Looking in your CACHE folder for the latest error logs MIGHT give you pointers as to where the system is being held up, and in some cases you can "repair" the damage that TM templates are notorious for...