Install New D-Link N750 Dual Band Router?

I just bought a new D-Link N750 DIR-835 Dual Band Router, and I tried installing it to apparently no avail. I used the installation CD and followed all the instructions carefully throughout, but once it was "working," I did a speed test and saw that there was absolutely no difference in speed.

I refuse to believe that this new router, which cost me over $100, would provide no noticeable difference over my old router. Speaking of my old router, I have the original router that Telus sent me for free. It's a Siemens Gigaset SE567, and I've dealt with it a few times when I had internet problems,fiddling with the 192.168.0.1 web address site, configuring the passwords and SSID, and the like. I'm not super-educated on the matter,but I know enough about it that with a thorough explanation, I could probably perform whatever is necessary.

Anyways, like I said, I followed all the instructions and after testing out some simple Youtube videos on both my tablet and laptop, through the wireless network that resulted, it couldn't even load a 480p video without lagging. I know that the router isn't the only thing that ensures speed, but even with my (probably barebottom) internet plan (which my father set up, not me, and knowing my father, it's probably the slowest connection available), I just cannot believe that the resulting network was the best speed available to me. So did I do something wrong? Are the routers interfering with each other? Is that actually the best speed I can achieve? Is that Gigaset even a router? Or is it a modem? Or both?