We had Bell TV, and Telus DSL before switching both to Shaw for significant savings. There is no reason why you couldn't hang onto Telus TV, and switch the internet to Shaw. We still have a landline with Telus.
Of course Telus will tell you all day long how their slower service is far superior, lol. Although if your area has Telus PureFibre, that's a way more attractive option if they'll price match Shaw, because Telus Fibre is now 175 Mbps both up AND down.
But yes, you can definitely hang onto Telus TV...maybe investigate Shaw though, just in case there is any savings to be had by switching.
And yes, it is that much faster. I came from Telus 25, and on Shaw 150, I consistently get 175 Mbps down, and 15 Mbps up. I'm paying less for 6X the speed.
If the coax cable was the problem, you'd see speed/connectivity issues throughout your home, not just one PC.
I was wrong, the $20 Gigabit NIC I bought off Amazon is now $15:
https://www.amazon.ca/TP-Link-TG-346.../dp/B003CFATNI
As long as your PC has a PCI Express port, it'll work, but they do sell the PCI version as well.
But if your PC is super old, I would personally either live with the 100Mbps on that one computer, or just replace the PC entirely. Unless you want to keep the PC around, and think the $15 is worth spending.