All the cable providers suck, some of the worst customer satisfaction rates in any industry anywhere. I have Comcast... and I even used to work for em long ago so I can say with some authority that the semi-regulated monopoly model is the source of all our misery.
Make sure you read your bills closely and understand EVERY charge. They'll overbill you and add fresh new bullshit services without even fluttering an eyelash. I recently needed a "defective" set top box replaced (they actually had sent a wrong back-level refurb model that couldn't do the job) so they could give me HD services and they went ahead and added a $10/mo "second adapter" charge along with shipping charges for the new unit. I got that all scrubbed. You have to bitch loudly to get all this shit fixed, maybe talk to multiple people or managers. I believe some of the customer service reps actually get commissions for these new services so they're deliberately adding the shit without telling you. Stay aware.
Can you read the specs along the side of the cable in the ground that needs to be replaced? Small pale white text, usually. Older cables weren't meant for broadband services and 300 channels, only the 50 channels or whatever from when cable was new. It's common and legit and good for you to get it replaced.
There are many cable types but RG-6 or RG-11 with good shielding is your likely replacement. Older RG-58 or -59 is thinner (not always noticeably) and shitty... if you have that, rip it out.
https://en.wikipedia.org/wiki/Coaxial_cable#Standards
For very short 5' or 10' lengths the older cable should actually not be a problem but it's cheap enough to upgrade, may as well. For longer lengths you'll
definitely suffer.
To troubleshoot the problem and isolate to that incoming underground link, plug your modem directly into it and eliminate all downstream cabling. Run those speed tests repeatedly. Chances are your tech dude is right and it just needs to be ripped up and re-run.
To eliminate signal hijackers (entirely possible, and they could be torrenting terabytes of movies or maybe they're infected with viruses and spamming the rest of the net) you need to login to the modem admin page and see all the connections. Use WPA2, never ever WEP. Use strong passwords. "!gm@otBS" is a good one (tho 12+ chars is better). "hunter7" is not.
Disable any remote admin capability for the device -- this allows hackers from the internet to break in if there are any vulnerabilities, and they get discovered all the time.
Ooops, I wrote a novel. Fucking caffeine.