1996 Lumina LS Sedan 3.4 V6 - Transmission problems

Hi, my Lumina, 115K miles, has had an odd problem for a while. Sometimes it will slip into neutral and I have no forward gears, the only way to get forward motion again is to shift into neutral, back to drive, and then wait a moment until it "catches". It usually does it when taking left hand turns or down steep hills (sometimes after sharp braking too).

This morning however it just lost drive all together and started making a nasty whirring sound, and I had to have it towed back home. Cannot get any gears at all :-( My wife thinks the transmission has completely failed and is a lost cause, but I think it may be something simple. Any ideas?