Unfortunately for you its a bad time to get a broken computer.
Well, it always is.
Main reason is AMD will release Zen in a few months (end of January atm), and with it comes a general jump in technology - DDR4, 14nm GPUs SSDs etc.
That means a lot of competition compared to the last years.
That said you cant create time and you dont have the money for those either.
For a 500$ Rig I strongly recommend a Desktop.
The cheap version would be an AMD APU like you have in your Laptop.
Yes, they are outdated. But that also is the reason why they are cheap.
You can get the current A10-78XX for just a bit over 100€ (150 Canadian dollar?)
Together with a cheap mainboard and 8GB of DDR3-2133 you can play every game, although current ones with low settings.
Then get a SSHD. That is a combination of a "old" harddisk with a SSD like cache. The 20 bucks more compared to HDDs are worth it and you cant get a full size SSD in your budget.
Together with case and the basics you should come out at definitely less then 500$ for a new Rig. Get a good blower for the APU for the rest and feel the near-silent best of APUs! (I have the lower TDP part and use passive cooling, no sound at all! And it plays Skyrim (old edition) with high settings.)
BUT that one wont give you lots of mining power or power gaming, thats for sure.
Getting an older Intel Quad computer with an dedicated GPU may be better for this. Cant give you tips for Canada though.
If you want to offset costs you might want to look at Suchflex:
That is still beta (feels more like alpha) though.
They also use Gridcoin, but you can "mine" that standalone. Unfortunately Suchflex atm still overrides standard BOINC installs. You can make it work, but it needs a few manual clicks every computer start then.
https://invite.suchflex.com/LennStar
Wow thank you for this comprehensive and information laden reply sir. I'll look into what you've laid out here as I start planning my build and it's components.