Car died and oil in spark plug wire tube

[horacus]

Well, I started the car and it idled for about 10 seconds and then died.
Tried to start it for a while but no luck.
The engine will turn fine but will not start.
I was gonna check the spark plugs and when I pulled the wires, one of the tubes has some oil on the wire.
I cleaned the oil but the car still would not start.
What should I do next?
Thanks for any help.

P.S. The car is 1989 Civic Si hb.

Edit:
Well, I did the valve cover gasket kit but that did not solve the problem.
A mechanic friend of mine had a look and the conclusion was that fuel was not being supplied enough due to a old/faulty battery.
After replacing the batter with a new one the starting problem is gone.

[Airjer_]

Check for spark

[horacus]

Ok, today the car started without problems and I drove it home from where I left it parked overnight, about 4mi drive.
So it looks like the only problem is the oil flooding the spark plug wires sometimes.
So I figure if I do the valve cover gasket kit which also includes the spark plug tube seals, it'll resolve the issue with oil getting into the spark plug tubes and onto the wires.
Is it something I can do in front of the house at the curb and without any special "honda" tools?
Anything I should watch out for?
Thanks.

[cherryelky305]

On some models you need to take the rocker cradle off to change the tube seals, if you need specific instructions i might be able to get them for you. I work at a honda dealer but I'm not sure on something that old.

[horacus]

Originally Posted by cherryelky305

On some models you need to take the rocker cradle off to change the tube seals, if you need specific instructions i might be able to get them for you. I work at a honda dealer but I'm not sure on something that old.

Thanks for the info.
I did the gasket kit today and after I lifted the valve cover I was able to change the main gasket, plug tube gaskets and the four grommets.
But the kit came with additional 3 rubber o-rings but I couldn't tell where those would go.
However, I'm still getting oil in #3 spark plug tube, it's not much but the spark plug wire is covered in oil.
The other 3 tubes are dry.
What could be causing it?
I'll check if the spark plug is all the way in but I doubt it wouldn't be.
Any suggestions?
Thanks