Is this the scenario?

* when the engine is off, the gear lever can move to all the gears, including reverse, and it feels normal

* when the engine is running, with clutch pedal pushed down, ditto

* engine running, shift to NEUTRAL, then let up the clutch pedal and car tries to move (i.e. lever in neutral position but gearbox is actually in one of the gears)

if so, it may be that one of the internal shift fork/pins has come loose or is cracked, so that when the lever moves it doesn't actually take it out of gear. This is a rare problem but not unheard of

especially if it only occurs between NEUTRAL and 1st/2nd (i.e. the 1st/2nd shift fork) while 3rd/4th has no problem