how many total parts are there in a basic ar15 if you disassemble it completely down to the last roll pin and spring?

Right at 200 I think.
Depends on the configuration.
Here's an A2.

A1, A2, or A3 (flattop) ? specify which type.

flash hider
washer (crush or peel)
barrel
barrel extension
index pin
FSB
front sight post
detent
spring
taper pins (2)
gas tube
gas tube roll pin
delta ring
weld spring
c-clip
barrel nut
handguards
upper receiver
ejection port cover
hinge
spring
c clip
forward assist
roll pin
spring
bolt
extractor
extractor spring
extractor insert
extractor pin
ejector
ejector spring
ejector roll pin
gas rings (3)
bolt carrier
gas key
gas key bolts (2)
firing pin
firing pin retainer
cam pin
pivot pin
detent
spring
bolt catch
plunger
spring
selector switch
spring
detent
take down pin
detent
spring
mag catch
mag release button
spring
trigger guard
trigger guard roll pin
pistol grip
pistol grip bolt
washer
trigger
trigger spring
trigger pin
disconnector
disconnector spring
hammer
hammer spring
hammer pin
buffer retainer
buffer retainer spring
buffer
buffer spring
receiver extension (carbine or rifle)
castle nut (carbine only)
end plate (carbine only)
spacer (A2 stock only)
bolt (A1/A2 stocks only)
stock assembly (A2 or M4)
carry handle assembly (flattop only)

front barrel sling swivel:
sling swivel
sling swivel rivet
OR
side sling swivel
back plate
spring pins (2)

....87

sorry, i'm interested in the number for an a3 flat top.