Okay, I have a few thoughts on this.
First, where the pin broke off, can the stub end of that's left in your tuner just be removed and replaced? These pins are usually just pushed in through a hole, and can be pushed back out with small pin punch. If you can get the stub out, you could just replace the pin with a small screw. If you're having a hard time getting the broken piece of pin out the wood, try first heating the pin by holding the tip of a soldering iron against it for a few seconds, then try gripping the end of the pin with small wire cutters, or flat-nosed lineman's pliers if there is enough sticking up.
Another thought is that you may be able to find another 'parts' Squier for cheaper than a new tuner. Lots of people have these things gathering dust, especially the Strats. People don't usually post their broken guitars for sale, but if you ask around you might be able to find something for free. The guitar in the post is in fact a Squier Strat that was given to me by someone who aquired it for free as part of a clean up job.
If you've got the money and want a little upgrade, you can buy whole neck assemblies online. Prices can range from $20-$250.
Upgrading the whole set of tuners is also fairly inexpensive, you can get full sets of tuners on eBay for less than $20, nice ones for less than $50.
Don't be afraid to just drill the holes in the headstock a little bigger, either. Even if the hole gets a little sloppy, the tuner post will eventually hit a stop point against the side of the hole and stay in place. Headstock is usually maple, and it can take a LOT of damage without much fear of splitting.
RE: A quick DIY guitar tune-up