If applying a new stylesheet doesn't change the appearance then it looks like the styling is local to each cell. If you have a look at the underlying expression of some of these input cells by going to the menu and choosing Cell > Show Expression you should see some StyleBoxes, as per this toy example using your code that you have supplied:
So if it is the case that all this styling has been introduced locally at each cell then go to the menu and select Edit > Select All to select all cells. Then select Format > Clear Formatting. This will remove all the local styling through out your notebook and your notebook will now respond to your choice of stylesheet.
Based on your feedback it appears other cells have localized styling as well and you want to keep that. So then you just need to clear the formatting for the input cells only.
Further inspection of the code you have been given reveals it to be a mess -- it is inputform without row boxes. With this information I'd actually recommend converting to standard form as per Mr Wizards answer but then your comments will be lost. Therefore I recommend the following, more laborious approach:
Make the input cell a text cell (or other cell).
Now make it back to an input cell.
Now clear the formatting.
Th screen grab shows the stages:
and to prove it works when I change the stylesheet:
If you have several of these notebooks these steps could be done programmatically but for a one off I'll leave it at that.