No... Not it doesn't mean it must be your laptop. They could have faulty equipment, not be well trained on using it, and usually they do the testing at the connection to your house, so there could be bad wiring inside your house causing it as well.
And like I said, all you're paying for is the POTENTIAL of 24Mbps, they're not guaranteeing you'll get anything even remotely close to that at all times. You may be able to download at 24Mbps, but the site you want to go to may only have say a 48Mbps backbone connection, and that has to serve EVERYONE who wants to access that site.
Also, depending on what you're doing, your ISP may well be throttling the activity. Even if they say they don't throttle or shape any traffic, odds are they're lying through their teeth. Comcast initially claimed they weren't doing anything of the sort, and finally when the evidence kept piling up all pointing to the same conclusion, they finally fessed up. Same with probably a dozen other ISPs, and those are only the ones forced to admit to it. Rather than invest in infrastructure to meet growing demands, they cheap out and buy some traffic shaping gear. IMO, it constitutes a breach of contract, but I digress.
Put simply, that 24Mbps connection, assuming we're talking DSL, is only between your house and the ISP. Once you go out onto the greater Internet, everything goes out the window. That is just the facts of life with the Internet. Anyone who knows more about networking than setting up a 2-3 system file sharing LAN will tell you the same.
Sorry to say, but you let yourself get taken in by the big claims and fantasies of being able to download files quickly. You're unlikely to ever come anywhere close to the speeds you think you should be getting, and it wouldn't matter if you lived right next door to the ISP's networking hub. What we sometimes fantasize in our minds when we see ads saying things like "Speeds up to 24Mbps" and what the reality will actually be, are generally very different.
Of course you say that their engineer only could get a 15Mbps signal, which you left out of your initial post... So, that just strengthens the argument that they are selling you a service which they know they can't provide. Best thing to do here, is drop to a lower tier of service that's as close to 15Mbps as possible. Play your cards right, and you might be able to get them to prorate your bill based on the differences in price given their own tech couldn't pull a strong enough signal.
Also, you never mention whether or not this is a cable or DSL service, or even something else. If it's cable, then you're completely and utterly screwed. If it's DSL, you can always hope some construction crew accidentally severs the line and they have to replace it, or that they'll maybe get a new DSLAM switch at the local hub. With cable, short of all your neighbors either moving away or switching to DSL or some other kind of Internet connection, you're screwed. Cable operates on a hub system. Everyone in a specific geographic region is routed through a specific hub, and each hub has a separate connection back to the home office. Usually something on the order of 100Mbps to 1Gbps, which EVERYONE on that hub has to share. Even if it were 10Gbps, you get 10-15 people with that same 24Mbps service package, and the bandwidth will get eaten up very quickly. If we're talking some kind of wireless/cellular service, then the shafting you'd get from Cable is going to look pretty good by comparison.
At no point during this whole discussion have I really seen anything that points to anything other than you allowing yourself to be taken in by the pretty ads and fantasies of downloading things very fast. Then reality came and kicked you in the teeth with it's steel toed boot. You can bang your head against the wall as much as you like, but unless you've been holding back on some crucial bit of info, I wouldn't be holding out much hope if I were you. This isn't what you want to hear, but it's more along the lines of what you NEED to hear. And in the unlikely event that one of the suggestions by the others actually improves things, then even better for you. Expect the worst, hope for the best.