It's possible to break everything by doing something so little for example renaming/removing the current theme without disabling it first.
It may also be the case that a new theme is installed which gives that white screen of death.
Hopefully fixing the problem should be painless if you have access to phpMyAdmin (or through SSH) with a few lines of MySQL
First, set Garland as default.
UPDATE system SET status=1 WHERE name = 'garland';
This alone won't fix the issue as the default theme is still set in the variables table and also more than likely in the cache. Change the variable value.
UPDATE variable SET value='s:7:"garland"' WHERE name = 'theme_default';
Then make sure the cache is cleared. TRUNCATE will drop all the rows in the cache table.