Your description sounds like a computer and charger that are operating as designed. There are three micro-controllers involved in battery charging -- one in the battery, one in the power adapter, and one in the Mac. This system is designed to never over-charge your Mac. The LED may be on the power adapter end, but it is controlled by commands sent from the Mac.
It would be green when I plugged it in and a couple seconds later it would turn orange.
Green -- indicates it is not charging, or possibly only trickle-charging. It may take all night or more to charge your Mac when green, or it may not charge at all.
Orange -- indicates it has started a charge cycle, and is doing a "quick charge". It may take only an hour or two to restore to "mostly-charged" state on a properly working battery. Your Mac will not start a charge cycle until the battery power remaining has declined to somewhere in the low 90-ies percent of its full capacity.
The numbers I indicated above are rough estimates, and assume the computer is OFF. If you are running it at the same time, it will take longer.