Chain skip
 

I'm a total bike mech newb. I have a Kona hardtail mountain bike. I commute to work and back year round with annual temps between -30 and +30C (-22 and 86F). Round trip is 10km (6miles). I have done this for 23 months. The original drive train is about 2500 to 3000km old. The rear derailer is about 1500km old.

For the last 6 months, I have had to start from red lights in an easy gear otherwise my pedals rotate but I don't move forward. I showed my chain to my LBS and he nearly kicked me out of the store because his tool couldn't even measure just how far gone my chain is. I replaced the chain and rear gears this weekend. Then I take my bike in my alley (it's paved), put it in a hard gear, stand up and try to accelerate quickly, once again my pedals rotate but I don't move.

Given the age of my drivetrain and the neglect, should I just go ahead now and replace my chainrings and derailer cogs?

You need to find out if the rear cogs rotate freely when this crank rotation is going on. If the cassette is moving freely like that, you need to service or replace your freehub. My guess is that the pawls inside are gunked up, and cannot always engage the ratchet teeth to give you forward momentum.

+1
Pawls may be chipped or broken.

Enjoy

Yup, freehub is probably in the same shape as your chain. Does it make any noise? I would expect it probably clicks like you're backpedaling. I'd inspect your chainrings (front gears) as well, I'm betting they're pretty worn.