Hello all,
#2 cylinder is dead, no compression! How does that just all of a sudden happen? No oil leaks/puddles anywhere.
How to repair?
Is it ok to run on 4 cylinders?

Engine has 168k

Lets assume your rings are OK and the valves are good, which is a lot of assumption. Verify the valves being OK by pouring about a table spoon of motor oil into #2 and checking the compression again. Using a drinking straw, about 2 inches of oil = 1 table spoon. If the compression goes up, the valves are good.

Unplug #2 spark plug and injector if you run the car on 4 cylinders. The car will cruise at highway speed OK, but with a significant loss of power.

It is always possible that #2 became flooded with gasoline due to a bad spark and completely washed to oil from the rings. But, you should have had a CEL pointing to #2 misfire.

Klaus
--
Always willing to listen, just not able to take direction.

P0304 code #2 cylinder. Dry/Wet compression tests yields no compression in cylinder 2. The other 4 cylinders ranged from 190-200 dry with a 10-15 increase in pressure during wet test. Stuck/bad valves? Next step?
I can see through the spark plug hole some carbon buildup on the top of #2 piston.

I need a history lesson. What kind of spark plugs have you been using? What kind of gasoline octane? Short, cold engine runs? Car sitting for a few months?

What I am getting at before pulling the head:

Short cold trips with cold spark plugs could result in carbon buildup on the valve edges. This results in a 'stuck' valve, meaning it will not completely close. Depending on the amount of build up, it can be broken off by revving the engine over 3000rpm for an extended period of time, AKA an Italian tune up.
High rpms will allow the valves to rotate and keep the seating surface clean.

If a valve is bent, nothing will help. Same for a broken or damaged piston ring. In either of these 2 cases, the head will have to be removed to find out what is wrong.

If you attempt an Italian tune up, leave the sparkplug connected and the injector connected. You want the possible combustion to burn off any dirt.

Klaus
--
Always willing to listen, just not able to take direction.

ngk standard plugs, regular unleaded gas, daily driver of 10-15 miles a day mostly highway.

You have nothing to lose, give it a high rpm 'tune up' after warming the engine up a little. I suspect you have a valve that isn't closing.

You also might want to do a Seafoam treatment to clean out the combustion chambers. Use a vacuum line that is attached to the vacuum tree, by the throttle body, and let the engine 'sip' a little Seafoam until the engine rpms bog down. Do not let the engine suck up a lot of Seafoam all at once!! Too much liquid will break a wrist pin! Just dip the vacuum hose in the bottle 1 second at a time. You can pour the remaining Seafoam in the gas tank.

Your cheap gasoline does not contain any cleaners, burns too fast, retards the timing, and the short commute never lets the oil temperature rise to above boiling. Ie., cold engine running at low rpms and cheap gasoline = cylinder carbon.

Klaus

--
Always willing to listen, just not able to take direction.

Did the Seafoam treatment which produced quite a bit of smoke at high rpm for a few minutes. Poured the remaining into the gas tank. Have been driving the past week, but no change. Still zero pressure in cylinder 2.
Any other ideas? As a college student I have no money for car repairs.

Probably a bad valve. I understand your predicament, I was a poor student also.

It might be time to unplug the fuel injector for the bad cylinder and run on 4 cyl just to keep any unburned gasoline from washing the rings.

Sounds like a good summer project! There are a bunch of pick&pulls in CT, so make a date when it gets warmer, find another 1996 and take off the head for future use. Good practice for when you do it to your own car.

Klaus
--
Always willing to listen, just not able to take direction.

How difficult is the head on an 850 for DIY'er? Is there a comprehensive step-by-step procedure somewhere on the web?

This is not a one day operation. The top cover is glued to the head, the glue acting as a gasket which must be cleaned off with alcohol, and then the cams fall out! Then the intake manifold and exhaust manifold come off before you remove the headbolts.

After removal, the head needs to be 'leveled' by a machine shop. Any valves to be replaced should be seated by same shop, not a DIY option.

Putting it back together is a chore. New head bolts, please! You can make your own special tools to hold down the cams so the cover can be glued back on.

The Haynes 850 manual has a 'good' writup for doing this for the 5 cyl engine. Just go to the local library and look at it.

Klaus
--
Always willing to listen, just not able to take direction.

Some time the rings seize up and cause "lawnmower syndrome".It usually affects more than one piston though.
Remove all the spark plugs and add about an ounce of light oil. I use Mystery Oil myself. Disconnect the coil and rotate the engine a few times. Let it set as long as you can, about a day. Check your compression and see if that helps.
Good Luck!!! RK