Files downloaded from piracy sites frequently contain hidden Trojans, spyware, or ransomware. These programs can log your keystrokes, steal financial data, or lock your files.
Websites that host fake codes often hide bad software. Downloading a file can infect your PC.
For version 3.40 specifically, the serial number acts as a digital key that ties the installation to a legitimate user license. In the era of this software's peak popularity, this form of DRM (Digital Rights Management) was standard practice to prevent unauthorized duplication of the program files.
Don't waste time hunting for a "working" online. The legitimate version costs about the same as a couple of coffees. If you cannot pay, free alternatives like Disketch, Avery Design & Print, or gLabels will serve you well without the security and legal headaches. Either way, you'll get your labels printed safely and ethically.