Unless it's been sitting upwards of 20+ years, breaks/tyres/etc will be in the same shape they were in when the bike was parked... so, odds are, probably fine. No offence to your parents, but the false memory that "It's no good" develops pretty quickly when you don't really want to dig out the old bicycle and go for a ride.
So what if you live on a hill? You think a more expensive bike will magically whisk you up there?
... okay, yes, yes it will, if you pay thousands of dollars for a fancy electric-assist model.
But you're not buying one of those bikes. You're going to take your crappy bike, shift into its lowest gear ratio, you're going to huff, you're going to puff, and... you're going to make it
most of the way up that hill! Sorry, but we've got to be realistic here. Give it a couple weeks and you'll be speeding up like nothing. I've always lived on hills; the grade here is such that in a car, your RPMs double when you pull off the main, flat road, and stay that way for the kilometre or two it takes to get here. People don't want to live here because they're afraid it's too steep for driving up or down in winter. I bike it every damn day. So can you!
Like any vehicle, the frame and the wheels are much less important than the motor. First get the motor working, then see if you need to spend money on the rest.
From googling (is it like
this one?) that looks like a fine city bike on the low end. It's the sort of thing I might recommend to a beginning commuter. As for getting it into shape: inflate the tyres. Do they hold air? Good! If not, you'll need to patch the tubes. A patch kit is only a couple dollars. Make sure you inflate the tyres to their manufacturer's rating, at least. If you have no pressure gauge, don't sweat it; you just want them to feel rock hard. To test the breaks, squeeze both handles to the fullest extent and try and push the bike forward. Does it roll easily, with great difficulty, or only after you break the tyres into a skid? You want one of the second two. Repeat with each brake individually and see if one has more stopping power than the other. If it's reasonably hard to push forward, you're fine! If it rolls easily, make sure that the pads are gripping the rims firmly; if not, tighten the cables. (It should be fairly obvious, but there's guides online for that.) Unless it was ridden tens of thousands of km before it got to you, you don't need to change the break pads. Test the breaks again. Stops better? Good. Now lube up the chain, go for a spin, and move the shifters through their full range. Does it shift into every gear, or at least most of them? If so, good! Enjoy your new bike. If not, clean any accumulated crud off the chain, gears, and dérailleurs, re-lube and try again. If that doesn't work, well, you get to go find a guide on adjusting dérailleurs. Most likely, all you'd need is to find the adjustment screws and a screwdriver to wiggle them half a turn or so. It's really not hard.
If this paragraph seems like too much work, facepunch. It's (at least!) a hundred dollars worth of bicycle you're getting free, and working with it earns you valuable skills you'd want with any bike, regardless of cost.
"But don't I need a better bike?" -- eventually, the crappy components on a department store bike will begin to fail, and it won't be worth it to replace them all. That takes at least a year of heavy daily use, though; usually more. By that point, you should be more comfortable with bikes and able to decide for yourself what you need (or just want).
