Putting in new, genuine Honda wires, plugs, rotor and cap
will cost about $90, tops, for the parts. www.slhonda.com 's
online parts store has very good prices for genuine Honda
parts, and that estimate is based on its numbers.

I am not trying to get you to throw away money. These
ignition parts, if old and worn enough, typically cause
running problems. In addition, they're due for replacement
every few years, anyway. So you spend the $75 now, and
eliminate these as the cause, or you spend it within a few
years. I do list a few tests below.

You do mean you swapped the entire distributor assembly
(cap, rotor, coil, igniter, and housing), right?

That's a good test you did. It does suggest the ignition
wires and plugs could stand replacement. Your test
eliminates the distributor coil from being a cause, which I
otherwise would have strongly suspected.

The distributor and ignition parts that are replaceable, and
how "testable" they are and whether they may cause running
problems, are as follows:

May cause running, but not generally start, problems--
distributor cap (not testable; costs about $20)
distributor rotor (not testable; costs about $7)
ignition wires (testable/inspectable to some extent, $50 for
all four)
spark plugs (inspectable, costs about $8 for all four)
distributor coil (testable to some extent, costs about $90)
distributor housing (not really testable, but the wire
harness, seals, etc. age, Costs about $250. People here
generally end up replacing these at least once in an early
1990s Honda's life.)
distributor etc. radio noise suppressor (testable, but it's
not clear whether all 91 Civics have them. $6)

May cause start problems, but not generally running
problems--
distributor igniter (testable; costs about $90)

For the ignition wires, with the car's hood up, run the car
in the dark. Do you see any sparking coming from the wires?
If so, replace them.

Then do a resistance check of each wire. They should not be
more than about 15k ohms each.

I have used non-OEM wires in the past, and I think they are
why my 91 Civic LX had coil problems. Reports here support
this, too. If your friend's Civic does not have genuine
Honda ( = OEM) wires, replace them.

I would still top off and properly purge the cooling system.

I would still at least inspect and clean with WD-40 or PB
Blaster the PCV valve.

I would still spend $6 for a bottle of fuel injector cleaner
and put it in the fuel tank, etc.

Any of these may solve the problem, at very low expense.

www.autozone.com has a free online manual for your 91 Honda
Civic Ex that can help in general with repairs.

www.tegger.com/hondafaq has some pointers on running
problems. IIRC, it says what I pretty much say above.