I would suggest leaving the actual connection alone.
Internet works with TCP/IP.
You can release the TCP/IP, and no live Internet any more.
Put in your Startup file a batch file, that contain the line: C:\WINDOWS\WINIPCFG.EXE /release_all
This will disconnect the Internet during Windows StartUP without actually disconnecting the Router.
Make an other Batch file that contains the line: C:\WINDOWS\WINIPCFG.EXE /renew_all
This file will reconnect the Internet. Make an icon for this file in a location known to you.
When you double click on this batch file, it will resume the Internet connection.
BTW: DHCP, and PPPOE are not mutually exclusive, they can exist at the same time.