It's a Toshiba Satellite C850 - B583
And I've had it for 4 years now, never changed the AC adapter before.
You should not have to replace the adapter/power supply/charger just because it is X number of years old. All electronics age over time, but 4 years is not that long for a charger - if it has not been abused.
My Toshiba A505 power supply still works great and I bought this notebook in 2010. What matters is the use and abuse it has had over its lifetime. My notebook got a lot of use through many miles, airports, hotels, and more the first year, then it has sat in the same spot for most of the next 6 years - plugged in almost full time since. If you are a busy road warrior, your supply may have gone through much more abuse, to include drops, kicks, large swings in environmental temperature changes, yanks on the cables, power line anomalies, etc. - not to mention, many many "deep" discharge/charge cycles.
If you remove your battery, can you run your notebook on just the adapter? If so, your adapter is most likely fine and the problem is more likely your battery. While I'm still using my original battery, my original 2 1/2 hour run times have dropped to less than 90 minutes per full charge. This is normal. If your battery has gone through many more charge/discharge cycles, it could very well be the battery. So again, if your notebook runs fine on just the charger, it likely is your battery.
And for the record, with all the problems with Li-ion batteries catching fire, I recommend getting an official Toshiba replacement
instead of trying to save a few $$$ with a 3rd party brand. At the very least, buy a replacement from a reputable supplier who stands by the products they sell. Beware of counterfeits.