Electrical – Identify the pins of the circuitry that resides within a laptop battery

Cells in devices that you do not wish to be a flaming ruin MUST have protection.
Having protection circuits does not guarantee it will not happen.

Cells without protection are intended for use by either manufacturers or experts or enthusiasts who add their own or for suckers.

Whole device protection and cell protection are complementary and serve overlapping but different roles.

4,000 mAh 18650 LiIon batteries are ~~~= 99.9% +0.1% - 0.0% sure to be rubbish.
ie not just < 4000 mAh but << 4000 mAh and low quality.
The people who bogus label cells

• almost never feel an obligation to use the best cells they can and

• almost always decide to add injury to insult by using junk as well as lying.

Real world experience shows that the value of 'almost' is very high in both cases.

Higher capacity cells can usually be fitted OK.
MUCH higher capacity will lead to long CC tails and overcharge but not an issue here as mAh_new is < to << 4000 mAh.

ADDED:

Notice that in this ad and all their other ads they ALWAYS show non-brand-label views of the battery.

However, you may find that the racing stripes and general colour scheme a good match for the well known "Ultrafire" brand batteries. This may in fact be a real brand and these may be real examples of it BUT you can buy empty shrink wrappers to apply to the battery of your choice with this (or other) branding on it , so caveat emptor. Better nullius emptor I'd hazard.

These ones are a stunning 6800 mAh - a steal at the price. Available here

You'll find others similarly arrayed here and
here - 3000 mAh and 4000 mAh and

6800 mAh !!!!!!!!!!!!!!!! {again}

and unspecified but with GENUINE CREE 2000 lumen {so 20+ Watt} flashlight for $9.27 and
only 4000 mAh and
that's better - 4200 mAh
and .............

Flee!

At 3.3~3.4V a 3.7V Lithium ion cell has practically no capacity left, and is past the 'knee' where increased current causes a large voltage drop. At this low charge state, small differences in capacity between cells also become significant, and some cells may drop their voltage before others.

In the graph below showing discharge of a typical modern 18650 cell at various currents, I have added a red dot showing where it reached 3.4V at 0.2C. At this low current the curve should be similar to open circuit - a bit lower but with a similar rapid drop. If you extrapolate and line up the discharge curves to meet at 0V then you can estimate what the voltage would be at higher current.

But what does this mean for determining "best" 18650 cells to replace the ones in your laptop? The laptop probably refused to start because the voltage under load went below the minimum it accepts. You don't know what that cut off voltage is, but you do know that the battery had practically no charge left, so it was past the 'knee' where voltage drops rapidly. So long as your replacement cells have a similar discharge characteristic they should be OK, and the exact cutoff voltage probably isn't that important.