There is no clear answer to the question of how old the Internet is. For different definitions of the “Internet”, there will be different starting dates.
For instance, it is commonly held that the pre-cursor to the Internet – ARPANET – could not be called the Internet. And it is true that ARPANET was not the same as today’s Internet even at the lowest possible level. But there is a commonality to ARPANET standards through Internet standards – the very first RFC (issued in 1969) to one of the very latest (RFC7115) are all part of the same body of work.
And whilst the overwhelming majority of ARPANET era standards have been superceeded, there are a few that are still valid today. For example, an early standard for the names of hosts which restricts what characters can be used is still valid and (for example) restricts the names that can be used in email addresses – see RFC608 (it has been updated but the essential restrictions remain).
The next milestone in the history of the Internet came when the older NCP protocol was replaced with TCP/IP in 1982 (actually the “flag day” was 1st January 1983); this immediately raised the possibility of joining networks together and to route between them. Previous to this, different networks had gateway machines which were connected to two (or more) networks. Before the Internet took off, there were more than a few precursor networks – MERIT, JANET, BitNET, …; all of which used different network protocols.
Gateway machines would typically only gateway certain kinds of application traffic from one network to another; typically email was the bare minimum leading to services which would send information via email – at one point you could even “browse” the web using email!
Routing on the other hand allowed end to end communication so it was possible to use applications directly.
The next milestone was allowing commercial traffic on the Internet. The earliest networks were founded for research purposes by the American military or academic organisations, and prohibited commercial traffic Until the core networks allowed commercial traffic we wouldn’t have seen the Internet as we see it today.
There are plenty of other milestones – some would include the foundation of the world wide web (in 1991 and not 1993) as one of the most important. I don’t; simply because it was something that was bound to happen in one way or another.