Engine seems to operate well. When trans. is engagedthe engine loads up amd lopes. Some have told me that a head gasket has failed. eng. 3.0 V-6, 71 K

The whitish gunky stuff is mayonnaise - an emulsion of oil and water and yes while it is considered to be a sign of a failing head gasket, it is often normal with some engines operating in cool damp conditions, especially when maintenance intervals are long and the engine oil is not among the best quality.

The presence of mayo can be considered no more than a clue to be stored away and used if other classic head gasket symptoms are displayed - excess amounts of cold start steam and water droplets from the tailpipe, a misfire on cold start that disappears fairly quickly, residual pressure in the cooling system of a cold engine and a steady coolant loss with no external leaks.
Generally three or more symptoms are needed, though residual pressure is a real indicator...

As the engine light is on a code read will be needed to begin the diagnostic process.

is it an oil leak or other fluid --under engine you have the oil filter - power steering lines-transmission pan ,lines -transfer case -front c/v axles and center ham -coolant-brake fluid-and gas all these lines are at the back of the trucks engine you need to look at whats wet and where to pin point a fluid leak best is by color trans-power steering usually redish --oil, transfer,axle,blackish ---coolant green or red --brake, tan

Below is a few notes I made to inform my customers about the cylinder head gasket. You might find them useful. Blue smoke is not typically associated with a failing head gasket.

I would guess the battery light coming on when the power steering fails is significant but I can;t tell you why. Certainly this is a major safety issue that needs to be properly investigated and the cutting out might also be related.

Cylinder Head Gaskets
A few explanatory notes...

The cylinder head gasket is a complex seal within the engine intended to keep cooling water, engine oil and the combustion process separate.

The life of a cylinder head gasket is very stressful and deterioration begins the moment a new engine is started for the first time and continues at a rate depending on the usage and the design of the engine.

It is almost inevitable that the cylinder head gasket will fail at sometime in the life of the engine and replacement will be needed.
Occasionally a complete head gasket failure is sudden (and disastrous for the engine as serious overheating can take place) but mostly symptoms or clues indicating the continuing deterioration of the gasket is resulting in it failing to do its job properly are present for a long time before complete failure occurs...

When two, or more, of the following symptoms are present most or all of the time it is time to seek help and advice: -

1. Residual pressure in a cold cooling system.
2. Pressure in cooling system immediately or very soon after start-up (while still cold).
3. Abnormal amount of bubbles seen rising through coolant expansion bottle (if it is clear plastic) while the engine is running.
4. Misfire occurring regularly on start-up that clears rapidly (cold or just-warm engine).
5. Steady coolant loss but no external leaks.
6. Abnormally large amounts of vapour from the tailpipe continuing longer than normal and might be accompanied by a spray of water. Some vapour and some droplets of water are normal, especially in cooler weather.
7. Unusual or erratic heater operation (warm/cold not electric fan) often accompanied by unusual temperature gauge indications.
8. Engine oil level does not fall in spite of usage or even seems to be getting higher: oil might also have a lighter coloured or creamy appearance than is usual.
9. Oily residue floating on top of coolant.
10. Emulsion present under oil filler cap and/or dipstick. Some emulsion (or mayonnaise) is usual for many engines under some circumstances.

Head gasket replacement is not a routine operation and it usually is not possible to predict the amount of work required before dismantling has taken place. For reasons of long term economy and reliability it might also be advisable to have other work carried out at the same time, such as timing belt replacement, valve stem oil seal replacement, etc.

It's possible that the old head gasket has de-laminated and the oil is passing through the inside layers of it. That is sometimes difficult to see.
Too late to check now but you should have checked the oil in the engine for coolant intrusion. Once apart, there always will be some in there so looking now is not valid. (why you always need to change oil after changing a head gasket).
Some '00 4.0L heads develop micro cracks that are difficult to find...it's possible you have an earlier head than the vehicle build year.
Also, have your radiator tested.... there is a transmission oil cooler in it if it's an automatic trans.
If it fails, you will also have oil in the cooling system, but it will be trans oil.
If you originally had coolant loss and steam from the tailpipe or you had a hydrocarbon test done on the cooling system I'd suspect the gasket or the head. If not, put the new gasket in and have the radiator tested. Same as coolant in the engine, if the cooler went bad, change the trans oil.
if it turns out to be micro cracking, either replace the head or use one of the high $ block sealers
to stop the seepage. 'Though I don't like using sealers, on micro cracks they seem to work pretty well if the directions are followed exactly..

POSSIBLE LEAKING WATER INTO ENG OIL CAUSING OIL TO BE SLUGISH DARK OR WHITE FILM COLOR, HEAD GASKETS OR WARPED HEADS

ENGINE LOPING CAUSED BY.LEAKING BY VACUUM LEAKS AT THE INTAKE MANIFOLD.CHECK ALL BOLTS ON THE INTAKE MANIFOLD TO MAKE SURE THEY TIGHT.YOU COULD HAVE LEAKING EGR VALVE OR PLUGGED PVC VALVE.DO A COMPRESSION TEST TO CHECK FOR LEAKING HEAD GASKET.DO A FUEL PUMP TEST CHECK FUEL PRESSURE.IT SHOULD BE 35 - 45 PSI.IF FUEL FILTER HAS NOT BEEN REPLACED.REPLACE IT FIRST IF FUEL PRESSURE TO LOW.DIRTY FUEL INJECTORS WILL CAUSE LOPING.TIMING CHAIN WORN.IGNITION TIMING OFF AND WORN LEAKING VALVES.AND WORN CAMSHAFT LOBES.ALL ABOVE WILL CAUSE ENGINE LOPING OR SHAKING.

Usually blown head gasket, could be a crack in the cylinder head or block.

Have you diagnosed the problem to be the head gasket, or are you guessing.

What are the symptoms.

I would be carrying out a compression check, and cylinder leakage test on all cylinders.

If it is a blown head gasket, it will need replacement, don't bother with any dodgy chemical sealer, it will not work.

Probably has a bad head gasket that is leaking between a coolant and oil passage.

Check the exhaust manifold gasket. I have a 2003 SVT Focus I had a problem with it loping at low RPMs. I had a free flow exhaust system. When I bought a new exhaust manifold I replaced the gasket and the problem went away.