Will my 96 chevy blazer run without the fuel tank vent valve?

Codes or no Evap Codes, the issue is in that system
You need a schematic of the evap system, so you can
test the solenoid or valves,mainly the vent solenoid, if that
applies Not the purge valve, that is up front & opens to allow
engine vacuum to draw out fuel fumes from the tank.

Gas cap is a common cause but GM does have a few issues with vent solenoids going bad as well as purge valves.

your tank is not venting properly. check along fuel line from tank to motor for a pressure relief valve to canister

the vent hose you are looking for is located off of the gas tank it should be beside your filler hose. if you don't see one there then you tank has a vent on top that is the problen and probably needs replaced

I have a 96 2wd chevy Blazer runs fine till i get about a mile or so up the road and then shuts down when i brake at stop sighns please help

p0443 is evaporative emission control system, purge control curcuit malfunction, p0449 is emission control system, vent control curcuit malfunction. p0449 is often a filler cap problem on fuel tank. try tightening cap

Do a compression test on all of your cylinders when it is cold. Backfiring is a sign of a worn valve seat allowing mixed fuel and air (lit by spark) to be forced back into the intake. You will probably see compression loss on one or more cylinders.

Also... there is a chance that the EGR valve is not totally seated when the engine is cold with just a small blow by. The EGR valve seats coke up over time with black gunk.

in the fuel tank

If it`s the one on top of the tank then yes it can be replaced without replacing the whole tank.In order to remove it you have to push down and counter clockwise.If you can`t get one at the dealer then go to the salvage yard and take one off a tank there.If it comes off you could get s check engine light.Good luck.

No, the fuel pressure valve may be stuck open so that the fuel pressure is too low when you start up, but the pump keeps up after the engine starts...
The fuel pressure valve is draining the fuel back into the fuel tank when the Blazer is parked.