The first step of checking your glow plugs is mandatory. Even if they were changed out last week. The valve clearance is really just good general maintenance anyways. Yet if totally neglected for a long period of time can have other consequences such as yours. .
As for your thoughts on your battery. Get it checked out somewhere as it's a free deal. No, boosting with a charger on top of a marginal battery is not a conclusive way to make sure you really have enough amperage available for the starter. A preliminary check of your glow plugs takes a meter and less than five minutes in your driveway. If it will not start with block heater assistance you do have a problem.