From the Vegas Help Centre:

Software activation and offline usability

After installation you are asked to activate the software by entering your serial number.
This step requires an active internet connection.

Following the activation of the serial number, the program will be registered in your user account. 
Serial number registration helps us protect our users from software piracy and grants users free e-mail access to our technical support service for a period of 12 months from the activation date.

After activation, the software will run also without an active internet connection!

The above relates to Vegas Pro, but the same process applies to MAGIX/VEGAS releases of Vegas Movie Studio Platinum.

Unfortunately, the reality is that you'll need to either fix the internet connection on your computer (usually fixed by reconfiguring the computer's connection to the modem via Windows 'Network Connections') or install VMSP17 on another computer with a functional internet connection.