Take a high daily dose of zoloft, you'd be able to sit and stare at a wall for 5 hours and be content
As to your main question, a complete lack of any neurotransmitters would kill you. The majority have involvement in breathing, circulation and digestion.
However if you had say, low enough levels to survive you'd probably
Dopamine: be a miserable paralytic mess, unable to learn or think, you'd have no motivation at all.
Serotonin: There was a study where a bunch of rats were genetically deprived of the serotonin 5ht1b receptor and put in a cage, They immediately attacked other mice viciously. There was also a man born with sepiapterin reductase deficiency, a genetic disorder in which the brain is deprived of an enzyme that is used in the production of serotonin and dopamine. He pretty much ate all day, had a messed up sleeping pattern, and overslept. Impressively he wasn't depressed, which says alot about the serotonin theory of depression.
Gaba: You'd have seizures and die. Or if you had just enough, be extremely anxious, restless, sleepless, and have cholinergic/glutaminergic excitotoxicity
Norepinephrine: You'd be extremely fatigued, not be able to move because of extreme hypotension and not be able to think or learn
Acetylcholine: Ever heard of datura?
Glutamate: Chronic fatigue syndrome
Endorphin: Extreme pain and depression
Thats only a few, theres a ton more i cant be bothered going into
Also if you lost your 5ht1b receptor and had low acetylcholine/low serotonin, you'd probably turn into a rabid zombie
http://www.sciencemag.org/content/265/5180/1875.abstract
http://mindhacks.com/2010/03/09/a-man-with-virtually-no-serotonin-or-dopamine/