It depends on how you define this - are we talking original source code that has not been altered for 40 or so years? Then the answer is yes, because there are plenty of old machines that were programmed in early times of the Internet, in a language most people dont' know to read or write anymore like COBOL (which was popular for accounting, so there are many old machines in financial-related companies), but because they fulfill roles too important for a company or government agency or research facility, some of them never got replaced. There are also computer enthusiasts who still use their old Atari 2600s and C64s and such, which were programmed to access the early Internet using acoustic couplers, even if this gets more complicated today (where I live, the whole telephone system has been digitalized).

Or are we talking general concepts that are used up to this day, that you can put into practice by any programming language? Or the protocols from early internet that are still in use?

What is "the Internet"? Is it also the wireless transmission of data? What about Morse code, then? Is it also analog telephones? What about dual-tone multi frequency signalling, then?

What is code? A programmer would say, coding is giving computers the algorithms for a specified task. Would a medieval Arabic algorithm of how to convert decimal to binary be code, then? This may not sound very Internet-related, but basically that's what inside a LAN cable: Ones and zeros, and there's a dedicated layer in the networking model (OSI model, or TCP/IP stack, if put into practice) that does just this: converting data to ones and zeros.

When it comes to standards that were developed and implemented with the usage for computer networks in mind, the most important two protocols, TCP and IP, are still in use. Both have been standardized in 1981 but were developed, and used for the first time, in the 1970s. New Internet standards are born with someone writing a theoretical paper for something that, in their opinion, should be a common norm, or a technical protocol, or an improvement of an existing standard. They suggest their papers to the IETF, an open standards organisation, as Request for Comments (RFC). There are archives of all RFCs online, but not all of them are standards. The oldest RFC still being a standard is, to my knowledge, RFC 20 (1969), which suggests the ASCII standard that is used to encode/decode binary <-> characters of the Latin alphabet (later versions also include other written languages). The text I'm writing is in ASCII, but will be converted to binary digits as soon as I type it in, and it will be converted from zeros and ones back to characters of the Latin alphabet you can read in your browser.