Stuck in 1st gear

If the engine wants to stall, it can only be because two gears have been selected simultaneously, which could mean that one of them is seized to the mainshaft.
The gear that actually still works must be seized or just not outshifting. In this case there will be no neutral, it will continue to drive in the same gear.
As for driving in other selected gears, it may be that your shifter is just not goinig thru the neutral gate, but more likely that one of the forks is just not properly installed.
In any case, you should be able to figure it out by removing the cover.
Finally, it is possible but difficult, to reinstall the cover with one of the forks not correctly installed.