To be fair, smartphones are as powerful as desktop computers from 1995 or so. (I'm guessing there, don't shoot me.) By definition, a smaller computer will always be less powerful than a larger one, so phones and desktops from the same point in time will never change in relative processing power.
My smart phone is more powerful than my netbook from about 5 years ago. My netbook is more powerful than my laptop from 10 years ago. My laptop from 10 years ago is more powerful than my desktop from 1995. 1995 Was roughly around the time the Pentium processors were just getting popular on the market. We're talking 100-200 mhz computers around this time. Maybe 300 if you were on the bleeding edge of the hardware. These computers would have in the tens of megabytes of ram. I believe mine from the period had 32 or 64. Comparatively my smart phone has 1 ghz processor and 1 gigabyte of ram... and it's somewhat of a budget model.
No shooting here, just saying you're vastly overestimating 1995 computing, or underestimating smart phones. My android phone can install a nearly full featured linux kernel and terminal emulator. I've known people who've run apache webservers off their phones. I personally use mine to VNC into my computer and, albeit slightly klunkily, manipulate my desktop from another room, or across town.
I have no doubt you could, with the right preparations, and the given setup that the setting provides, do anything this guy was doing, present day. It's the preparation that'll get you and the fact that odds are, as soon as what you're doing is noticed, you'll be cut off pretty quickly, and anyone half way competent will patch whatever security hole you exploited, making most or all of your preparations meaningless.