I don't even need an expensive laptop

Hey everyone, I noticed things have gone pretty quiet on the forum lately... but I figured I'd try to shake things up anyway.
So, here’s the situation: my four-year-old laptop (HP 635) is basically on its deathbed. The keyboard has been acting up for a while now, and now the hard drive has finally given up the ghost; it still boots into Windows, but there's a mountain of bad sectors and other issues, so it's really just a matter of time before it dies completely. I know, I know, I shouldn't be bringing this up right now—I realize the drive and keyboard can be replaced—but I was thinking if I sell this old thing for whatever scrap value I can get and toss in a little extra, I might actually be able to pick up something new.
It's easy to act like a genius when you've got a massive budget, but my funds are capped at about $833. Ideally, if I could swing it, I'd love something with an i7, or maybe 8GB of RAM, or whatever modern processors are out there, and definitely an SSD from a reliable brand like Asus or Toshiba and such.
But like I said, money isn't the issue—it's the lack of it.
Anyway, how am I supposed to make sense of $2,500? What’s the best move here...
To give you a bit of background on me, I don't play games, so a dedicated graphics card is useless to me. It’s mostly just browsing the web or the occasional download, though I do that less often now since my Sony 808 C running on an Android TV platform handles all my Kodi needs (long live Kodi and streaming!) and YouTube. Occasionally I'll jump online to browse or pay some bills. Come autumn, my daughter will be starting school, so she might use the laptop occasionally for basic schoolwork.
In reality, I don't actually need a high-end machine.
The HP 635 wasn't bad back when I bought it for roughly $833, and it served me pretty well for a long time.
What I want to know is: should I avoid Intel Celeron processors at all costs? Everyone seems to say they're garbage. I'd prefer a Pentium or maybe something from AMD. I'd also like at least 4GB of DDR3, which is what my current junk pile has. I don't need anything fancy, but I would like a webcam. As for storage, I don't need a huge drive, maybe 500GB max.
I'm also looking for something at least 15 inches. If anyone is willing to lend a hand, I'd appreciate it, as my technical knowledge is pretty surface-level at best. Thanks.

These are the ones I'm eyeing. The first one has some extra discounts that would make it a much better deal than the sticker price, and the second one has a promotion for a 5-year warranty, which sounds pretty great.

http://www.walmart.com/multimedia/laptops/

http://www.amazon.com/informatika/laptop-deals

So, maybe this one could work, especially if there’s an extra discount on top— Acer E5-573G-P7NS notebook Price: $833

To be honest, I don't think Walmart really has a great selection, and their prices always seem a bit high!
Maybe at Best Buy, with a 5% discount, you could find something like a Lenovo or maybe a Toshiba with an Intel Pentium N3540 that fits within that budget limit.

Just a heads-up though when looking at Lenovo! For instance, this IdeaPad 100-15IBY model (80MJ00DASC) also uses the Pentium N3540, but I've read it has a pretty terrible build quality. The reviews are actually quite bad because the chassis feels cheap and it tends to overheat like crazy.

Then there's also this Dell with a 5% discount

You can actually find some decent deals at Walmart, especially if you use those discount points and pay in cash, obviously...

Regarding processors, stay away from AMD because their chips in this lower price bracket are absolute garbage. You should also steer clear of dual-core Intel processors; they’re just too slow and sluggish for even a basic setup—you know, the usual stuff like Windows, running an antivirus in the background, Office, browsing, YouTube, maybe some music, and a light download here and there. Dual-cores just can't keep up with that. So, if you're looking at Pentium or Celeron, make sure they're quad-core. A combo of 2 physical cores and 4 logical cores works fine too.

That means you should be looking at the 3825U, N2930, N2940, N3530, N3540, N3700, and any i3 processors. Just stick to those.

As for brands, it basically breaks down like this: Dell is top tier because they come with a 3-year warranty. Asus and Toshiba are second tier since they offer 2 years plus extra coverage through Asus Promotions and Toshiba NMWT. Then you've got Acer, followed by Lenovo, and finally HP. With HP, you have to watch out because sometimes they give you 2 years and sometimes just one. Also, don't fall for those "deals" promising 4 or 5 years of coverage; those aren't actual manufacturer warranties. They're just service contracts you sign when you buy the laptop, so check the fine print because they aren't the same as a factory warranty.

If you happen to stumble upon a laptop within your budget that has a dedicated graphics card, it’ll most likely be an Nvidia 820 or 920, maybe an 840 or 940. That's better because a dedicated GPU lets you throw on some simple games, and since it has its own memory, it doesn't eat into your RAM, which helps the whole laptop run smoother...

Check out Elipsa, Architect, AMD, Chipotle, Links, Walmart... maybe Amazon too. And definitely check out Nabava; their filters are great so you can really dial in your specs...

If my memory serves me right, Lenovo offers a standard one-year warranty across their entire lineup. On top of that, Best Buy is currently running a promotion where you can snag an extra couple of years of coverage for next to nothing on a huge selection of models—not to mention you can shave another 5% off the price if you just order through their website.