I might understand what the issue is, but I'm not entirely sure.
(Very slight spoilers)
When you delete the "save game" file, you should be faced with the main menu screen from the beginning.
Upon selecting start, the game should begin as normal.
The game proceeds as (mostly) normal until a certain area in the Barrens.
If the issue is that the game doesn't seem to remember Niko waking up and leaving the tower, I'm not entirely sure what's going on. Maybe try making sure the game has access to the files it needs to read?
Sorry if this doesn't help.