Chainsaw will start but when I squeeze the

I expect the design of your new chainsaw will be similar to many small engined tools where owners often discover they need an extra hand.

Usually the throttle is opened (trigger pulled) and then the trigger lock is pressed and the trigger released. The lock will hold the throttle partway open; freeing both hands to hold the tool steady and pull the starter. The partway open throttle makes starting easier and once started, the engine will run fast aiding a quick warmup and less chance of dying or fading.
Once the engine has warmed enough so the choke can be disengaged, a quick squeeze of the trigger will allow the trigger lock to disengage...

Check fuel filter, fuel tank vent and possibly clean carb and replace carb diaphrams

I'm guessing from the statement that it "will not work to increase speed" that you have been able to successfully start the chainsaw.
I have to look at this with the assumption that you haven't run a chain saw before, so bear with me if some of this is excessively simple.
If the throttle trigger does not move, something is jammed. The handle for the choke should automatically move to the retracted position when you pull on the throttle. If it doesn't, see if the trigger will move after you push the choke handle back in.
If the trigger moves in when you squeeze it but you don't hear any change in the engine sound then it's probable that the throttle wire has disconnected at the carburetor or at the handle.
Is the chain brake off? You need to pull it firmly back toward the upper handle for it to be disengaged. If the handle is forward it will lock the outer portion of the clutch. If you try to accelerate with it locked the engine will bog and not allow the chain to move.
Any of these conditions other than the chain brake will probably require some disassembly. Make sure you're confident that you've correctly reassembled everything if you're going to do it yourself.

Check the fuel tank vent. Does the saw leak fuel when laying on its side.? Faulty vent can cause the saw to bog down when running

change your plug !

The possibilites are 1. dirt or water in the fuel; 2. filter in fuel tank clogged; 3. main mixture screw set too lean. I am presuming you have the correct petrol/oil mixture.

15 years old...

One cause to look in too is a leaking seal around the crank, this is causing a vacuum leak.

Hope this tip helps.

R/
David

First thing,
Check the air filter, once checked, & clean/replaced,
Adjust timing.
This is a very easy job to undertake on small petrol engines.
1: adjust the gap between the contact & the magneto,
2:Or adjust the space on the tip of the plug.
So simple.
Fixed'Ya!
& don't forget to rate:)!

Hi, are you pumping the primer, till it's full, before starting?