Has lost most of its power when you give it gas

Still sounds like the pilot system in the carb is not clean... these are TINY passages.. several of them too! .. some hidden by blind plugs that have to be removed to properly clean the carb!!! If you are not sure how to do this.. take it to a professional!!!!

Old fuel, dirty carb jets. Low fuel level in carb. Has it been sitting up? Check air filter and plug.

The high speed jet isn't rich enough or the carb passages needs to be cleaned. You can move the clip down one spot on the needle so it gets more gas, this will also give you more power at the top end.

Check all Sensors like airflow sensor Water sensor ,oil sensor . when the warning light comes on it sends half load power to the cdi

you might have a dirty carb.check the big jet in there as it might have a blockage.sounds like you have enough gas going through the small jet to start the quad and for slow speed but when you want to give it good power, it starts to bog down.do the carb thing first

try cleaning the carb.

Bad battery

First.. check the compression..>120PSI...
Why did you replace the carb..???? that was unnecessary.. carburetors don't "just go bad"..
Stop playing mechanic.. take this ATV to a QUALIFIED professional!!

Adjust the fuel idle and the accelerator cable.