First of all, gaming laptops aren't really good compared to gaming desktop PCs; I know you're asking for a laptop, but you can consider desktops too, as they are cheaper and usually more reliable. Only downside is they are obviously not portable and use a bit more energy, but you could keep your Toshiba just in case you need to do simple task while being away from home or something like that.
Second, if your computer is 4 years old or more, it'd be better for you to just buy a new one. Updating your laptop might be annoying, specially if it's old. I can't really tell what's wrong with what you said, but I'm guessing it's mostly your CPU because it can boot but then just slows down, so I'll have to agree with thegoodhen.
PS: I just read you had your hard drive changed, so yeah, it must be the CPU or just maybe a faulty mother board. And for recommendations, I'm not really an expert but I have heard Asus are pretty good though I can't tell from experience. What I can tell is that Dell are usually cheap and reliable, you see them everywhere nowadays. I have an Inspiron 6400 since 2006 (I'm kinda poor too) and it still works like it should. Only thing that died was the battery, but batteries always die anyway... HP is also okay, but you have to choose in the end. Or you can also tell us more about what you'll be using it for if you want a more specific recommendation.