Ok, so, context: My laptop (Dell Inspiron 7000 or something like that) is a little old now. I got it about two and a half years ago, and apparently, that's a long time in laptop years. I am fairly rough on my stuff, so it's more than a little worse for wear: in fact it has some serious structural damage (mostly with the screen and frame). I've had it repaired a few times and replaced the screen a few times; it's not great off now, but the main issue tends to be with the screen than anything else. All of my problems with it have been limited to physical damage on the screen or around it, or to wifi, never to power or battery or anything along those lines.
Cut to a few weeks ago, I started having issues with freezing. This universally happened during games, and always took one of two forms: 1) my computer would become completely unresponsive save for holding the power button to shut it off, 2), it would simply turn off with no prior warning as if I had been pressing down on the power button (like if I had unplugged a desktop). It's started happening fairly frequently, such that I find myself unable to play multiplayer games for extended periods of time without a crash. I tried a program that would let me read the crash reports, but I found that there apparently aren't any, even though it is set to do so (there might have been a space issue? My computer is pretty full...).
So my question: what do I do? I've heard suggestions of an overheating issue, but while it does seem to get kinda hot, my skepticism with that is that it's never happened in all the time I spent playing games on it before, and this started in the middle of the coldest part of the winter so far (Below 10 Fahrenheit). I guess more specifically, my question is: what should I do to try and figure out what's wrong? I'm completely willing to open my computer up (and have done already, both to upgrade and repair) and do repairs or anything else, but I'd rather not jump down a rabbit hole like that unless I'm fairly certain that's where the problem is going to be. Could it be a memory issue? Something with the hard-drive? Wires going undone, or graphics card crashing, or dust, or fan, or what? Hardware, software? I just don't know where I should look.