Help me fix my internet speed?

[Haiajue]

I'm pretty good with computers but I don't know the first thing about networking.

Background:

We have DSL. Our speeds were just fine until a few weeks ago when it started acting up and we couldn't connect at all. My mom went out and bought a new box (not sure whether to call this a router or a modem). We can connect to the internet again, but our download speeds are inconsistent. Pretty much the only thing our internet is good for now is browsing web pages (which is fine for my parents, but not for me). Streaming videos takes FOREVER, and playing any game that requires an internet connection is impossible (constant lag spikes that will last 10 minutes to an hour, with possible disconnects that occur frequently).

Can anyone help me fix this? My mom has called our ISP multiple times and she says everything is fine, so it's obviously a problem on our end. I've run a speed test before and our download speed and everything was fine at the time, it's just very inconsistent. I'll try downloading something later and our speeds will have dropped to 30 kb/s. Games may be playable for 15-30 minutes or so, then they become unplayable for an hour; rinse and repeat.

If this will help, we have a ZyXEL P-660HN-51 (router? modem?). Today is my day off so I'll be spending all day trying to fix this. We also all connect to our internet wirelessly; my parents have laptops and I have a wireless USB in my desktop. The wireless USB is pretty old but I already tried using my desktop and my parent's laptop with an ethernet cord plugged in simultaneously, and both would lag at the same time.