I have a hypothesis on how computers could gain sentience

[Mr Greene]

Neurons using electrical signals is more an analogy than an actual fact.
They are also rather more complex than simply on/off switches. 
There are 27 different neurotransmitters and over 50 neuroactive peptides:

Agmatine
α2-Adrenergic receptors, imidazoline receptors
NMDA receptors

Aspartate
Asp
–
NMDA receptors

Glutamate
Glu
Metabotropic glutamate receptors
NMDA receptors, kainate receptors, AMPARs

Gamma-aminobutyric acid
GABA
GABA receptors
GABAA receptors, GABA-ρ receptors

Glycine
Gly
–
NMDA receptors, glycine receptors

-serine
Ser
–
NMDA receptors

Acetylcholine
Ach
Muscarinic acetylcholine receptors
Nicotinic acetylcholine receptors

Dopamine
DA
Dopamine receptors, trace amine-associated receptor 1[12][13]
–

Norepinephrine (noradrenaline)
NE, NAd
Adrenergic receptors
–

Epinephrine (adrenaline)
Epi, Ad
Adrenergic receptors
–

Serotonin (5-hydroxytryptamine)
5-HT
Serotonin receptors (all except 5-HT3)
5-HT

Histamine
H
Histamine receptors
–

Phenethylamine
PEA
Human trace amine-associated receptors: hTAAR1, hTAAR2
–

-methylphenethylamine
NMPEA
hTAAR1
–

Tyramine
TYR
hTAAR1, hTAAR2
–

Octopamine
Oct
hTAAR1
–
 
Synephrine
Syn
hTAAR1
–

Tryptamine
hTAAR1, various serotonin receptors
–

-methyltryptamine
NMT
hTAAR1, various serotonin receptors
–
Anandamide
AEA
Cannabinoid receptors
–

2-Arachidonoylglycerol
2-AG
Cannabinoid receptors
–

2-Arachidonyl glyceryl ether
2-AGE
Cannabinoid receptors
–

-Arachidonoyl dopamine
NADA
Cannabinoid receptors
TRPV1

Virodhamine
Cannabinoid receptors
–

Adenosine
Ado
Adenosine receptors
–

Adenosine triphosphate
ATP
P2Y receptors
P2X receptors

Galanin
GALR1, GALR2, GALR3
–

Galanin-like peptide
GALR1, GALR2, GALR3
–

Gastrin
Cholecystokinin B receptor
–

Cholecystokinin
CCK
Cholecystokinin receptors
–

Vasopressin
AVP
Vasopressin receptors
–

Oxytocin
OT
Oxytocin receptor
–

Neurophysin I
–
–

Neurophysin II
–
–

Neuropeptide Y
NY
Neuropeptide Y receptors
–

Pancreatic polypeptide
PP
–
–

Peptide YY
PYY
–
–

Enkephalin
δ-Opioid receptor
–

Dynorphin
κ-Opioid receptor
–

Endorphin
μ-Opioid receptors
–

Endomorphin
μ-Opioid receptors
–

Orexin A
OX-A
Orexin receptors
–

Orexin B
OX-B
Orexin receptors
–

Secretin
Secretin receptor
–

Motilin
Motilin receptor
–

Glucagon
Glucagon receptor
–

Vasoactive intestinal peptide
VIP
Vasoactive intestinal peptide receptors
–

Growth hormone–releasing hormone
GHRH
Growth hormone–releasing hormone receptor
–

Somatostatin
Somatostatin receptors
–

Neurokinin A
–
–

Neurokinin B
–
–

Substance P
–
–

Neuropeptide K
–
–

Adrenocorticotropic hormone
ACTH
ACTH receptor
–

-Acetylaspartylglutamate
NAAG
Metabotropic glutamate receptor 3 (mGluR3)
–

Cocaine- and amphetamine-regulated transcript
CART
Unknown Gi/Go-coupled receptor[14]
–

Bombesin
–
–

Gastrin releasing peptide
GRP
–
–

Kisspeptin
GPR54
–

Nitric oxide
NO
Soluble 
–


CO
–

Heme bound to 

H2S
–
–