Unstable internet connection

Checking my ping via Microsoft command prompt, and instead of the usual 2 ms, I’m seeing this (Slika). Sometimes it even spikes over 190 ms; it just fluctuates constantly.
I don't think this was an issue before, but it definitely started once they swapped out my modem for the exact same model.
It's been going on for about five or six months now.
The same thing happens on my other computer, which is also on the Wi-Fi. Even though that one is only about 2 feet away from the modem, the results are identical.
When I plug in via a Local Area Network connection, the latency stays steady at 1 or 2 ms without any jumping around.
I even downloaded 'InSSIDer Home' and tried manually adjusting the channels in the modem settings, but it didn't help at all.
I called my provider (AT&T) and they basically told me everything looks fine on their end. They said if I want a new modem, I'd have to pay for a technician to come out and prove there's actually a fault, blah blah blah... I can't remember the specifics, but basically, they claim everything is perfect when it clearly isn't. :S
It's causing major lag whenever I try to play games.
So, my question is; since I have an old AT&T modem lying around... can I swap it out for this AT&T one, or maybe find another way to use it? I'm pretty sure the issue is definitely with the modem they provided.

Did you try a factory reset on the router yet?

Yeah, nothing.
EDIT: I actually started another thread about my internet connection issues, but we couldn't quite get it sorted out. So now I'm just wondering if there's any way to swap out this modem or something similar, like I mentioned earlier?

Either way, you can just unlock AT&T's gear and set up some kind of bridge... plug in a LAN cable and broadcast the Wi-Fi from there.

How do you think I should go about unlocking it?
So, would that actually improve the signal? If so, I don't really need it—my connection isn't dropping, it's just that the ping keeps jumping around like I mentioned before...
Sorry if I misunderstood you, but I only know the basics when it comes to networking and all these gadgets... Can I just swap out this Microsoft one and use my AT&T modem instead? Because from what you said, it sounds like the AT&T one would just run through the Microsoft modem and boost the signal, which isn't my problem since the signal is fine. I think I should just ditch the Microsoft modem altogether and put my other AT&T modem in its place instead...?
I'm definitely not an expert on all this internet stuff.. 😁

The issue is that ISPs usually bake some proprietary software right into their routers just to get you online. Not sure if AT&T does that with the H1, but my money's on yes...🕺

Since we haven't made much headway on that issue, I've got a different question for you all. I have a Gigaset's SX768 modem lying around—any ideas on the best way to put it to use? Also, if it's possible to set it up as an access point, could someone point me in the right direction on how to do that?