iMac (27-inch, Late 2009) Trouble Installing New Operating System

It seems your internal drive is showing an image of the installer DVD volume. While booted to the Snow Leopard DVD, you will need to partition & format the whole physical internal drive using the instructions in the following article:

https://eshop.macsales.com/tech_center/formatting/Mac_Formatting_6-10.pdf

FYI, a Late-2009 iMac should be able to boot into Internet Recovery Mode using Command + Option + R to access the online macOS 10.13 High Sierra installer assuming that macOS 10.12.4+ was installed on this computer at some point in the past. You will likely need to use Fix #3 from the following article in order to bypass the "Recovery server could not be contacted" error message:

https://mrmacintosh.com/how-to-fix-the-recovery-server-could-not-be-contacted-error-high-sierra-recovery-is-still-online-but-broken/

Unfortunately some Macs may only boot to the online installer for the version of macOS which original shipped on the computer from the factory (in this case it would be macOS 10.7 Lion since that is the oldest online installer available) regardless of the keys used to boot.

Mac OS X 10.7 (Lion) may be the oldest version of Mac OS X available for download from Apple, but it Is not the version of Mac OS X that shipped with Late 2009 iMacs.

Late 2009 iMacs shipped with Mac OS X 10.6.* Snow Leopard, and with optical recovery discs. Originally, there was no such thing as a Recovery partition or Internet Recovery. If your internal drive got completely messed up, you needed those optical discs (or some other working copy of Mac OS X on an external drive) to recover.