 credit card!
To put that into perspective, there's three parts in play here: 1998, her dad's credit card, and the software engineering knowledge and tools required to build what Google built in 1998. Let's start with 1998: The internet was much smaller back then. By the end of 1998, Google had an index of about 60 million pages, and Larry Page's web crawler had been exploring the web since 1996. The total amount of data downloaded was probably in the ballpark of 200 gigabytes by the end of 1998. Storing 200GB of data on 33 bleeding edge 6GB hard drives at $370 a piece would have cost about $12,210 non-inflation-corrected at that time. That's without the hardware, electricity, nor bandwidth to actually operate machines to fetch and store the data. In 2009 you'd have gotten a 1000GB drive for $74.99 and could have run it from a single computer, while people regularly download more than 200GB a month on unlimited cable broadband.
So getting the data had become cheap enough for our hypothetical teen's dad's credit card. Crunching the numbers would require a few more resources, but 1998's internet was small enough to be crunched on EC2 with her parents's credit card. Serving the data and answering queries on a popular website without feeling sluggish would also require a few more servers. Let's assume 30 servers would handle the peak load for a start (Altavista was running off 20 multi-processor DEC 64-bit Alpha's in 1998). At not-the-cheapest-at-the-time $70 per server-month on Amazon, that would give us an estimated cost ceiling of $2100/month, with the expected cost being more along the lines of $500-$1000/month. Now I'm sure Dad wouldn't appreciate it, but for many people that's in the ballpark of what they pay for rent and thus affordable.
So theoretically speaking it could have been done in 2009. More than that, price-wise it probably could even have been done in 2006 without ever touching any hardware yourself. But of course money wouldn't have been the only difficulty for a hypothetical fourteen year old trying to build Google in 1998 or even 2009. Just because you can build anything you want in theory, doesn't mean you know how to do so in practice.
But not only has hardware gotten cheaper and easier to handle (through software), but during the same time our collective understanding of best practice software engineering has progressed by leaps and bounds as well. In between 2006 and 2009 many more people became acquainted with highly distributed architectures. More tutorials, libraries, and opensource software were written than ever before. Distributed Databases and NoSQL systems garnered a lot of attention. And with distributed version control systems like Git, code reuse and collaborative development became more commonplace. Many people stopped thinking about how to program individual computers altogether, and started thinking only in networked systems. Because of the wealth of information and code available, and a large community concerned with distributed system problems, a lot of things that were difficult a decade earlier, had become fairly easy to do.
Somewhen towards the end of 2009 I realized that writing Google as it was in 1998 didn't seem as daunting a task anymore. Not only was the hardware cheap, and the information on how to do it widely spread, but a lot of the functionality had already been implemented. Distributed Datastores? Check. Batch Data Processing? Check. Web Crawlers? Check. Web Servers? Check. The age of big data had arrived, because self-taught kids who wanted to could now play with it without asking for permission.
So do I think a fourteen year old could have pulled it off? I sure think so, but I realize in 2009 it would have taken a very tenacious fourteen year old. But that was 2009. If you are skeptic about my predictions for the past, how about applying them to today or 2015? How long till the technology that, at the time, precipitated the fastest wealth generation humanity had ever seen, can be replicated by a teenager with next to no budget during summer break? How long till it's s