If you lost your city and it wasn't invaded by enemies, then it was because your population decreased slowly each turn until the city disappeared. Here is a list of everything that could cause population decrease (in no particular order).
-Build a colonizer (a unit that creates another city). This brings your population down by 1 point every time you build one. I think we can rule this one out.
-Weapons of mass destruction. We can rule this out because you were early in the game.
-Aliens attacking an ungarrisoned city. This may have happened.
-You don't harvest enough food each turn to feed all the people. In this case, you lose one population point per turn until you balance your food by either placing more laborers as farmers or using formers to construct farms. This may have happened, but it couldn't have been the only thing because eventually you would have had enough food again because there is an automatic +2 food bonus that the capital gets. So even if you disabled all you farmers and lost a lot of people to starvation, your capital still would have leveled out around size 2.
-You accidentally clicked the "raze" button which deliberately slaughters 1 population size per turn. It keeps doing this every turn until the city disappears or you turn it back off.
It's difficult to conclude what happened in your case. I'm thinking that you either ran out of food (down to size 2) and then got attacked by aliens
or you were razing your city on accident. You will be much more informed if you read all the notifications at the right-hand side of the screen at the beginning of every turn.
About your morale issue: There are a few situations that will give you an automatic -20 morale (more or less).
-State of starvation (this is possible)
-State of being razed (this is possible)
-State of recently being captured by enemies (this is not possible because you started with this city.
As I mentioned in that other thread, morale will give you percent bonuses or penalties to everything you harvest, mine, produce, research, and tax. So having such a huge negative morale would account for your "nothing's getting done in my capital" situation. You tried to lower your tax to balance things out but the truth is that -20 is just too huge. You need to find out what is causing it and fix it. Like I mentioned before, hover over the morale in that city and read the tooltip. It will tell you where all the negative morale comes from.
I'd just like to reitterate everything I said on that other thread (the second page of
this thread).
Also check out
this thread about Morale.