Broken dock connector on iPhone 4

Sadly you are out of luck, but it was a good idea!

Apple transitioned fully to charging over USB only, although for a while both Firewire and USB charging were an option. This caused a bit of a row when it happened, because for years 3rd party manufacturers for charging docks and speaker docks etc never bothered to update their designs to use USB when warned that the Firewire was being deprecated by Apple. So when they took out the relevant internals to support Firewire charging, you started to see messages like "This accessory is not supported" and your device would suddenly no longer charge because the USB pinouts had not been internally implemented.

However, naturally the 30 pin pinout of the dock connector remains the same spec, but referring to it does not mean that all functions that the cable specification supports will be available to the end device, and in your case an iPhone 4 will only charge over USB.

I'll link you to a separate Q&A here that might assist in cleaning your connector up to make it work, sometimes a rigorous clean is all that is required.