Furniture, Wood and Cabinetry Finishing - problem with newly painted desk, what next?

We painted an old desk to be used in our young boys room as a computer desk. We stripped it down to bare wood, sanded and painted with an
oil based enamel (Enterprise Interior Oil Semi-Gloss Enamel, Valspar Corp.),
exceeding the recommended drying times between 2 coats.
We went with oil because we wanted a hard surface and everything you read suggests that oil based paints produce a harder finish.

Anyways, much to my surprise the desk shows fine scratches easily. It has been 2 weeks since I painted it and if I lightly run my very short and not sharp fingernails over the surface it produces scratches. I went around the house doing the same thing to several other painted surfaces including a small table I painted with spraycan acrylic years ago without once producing the same scratches.

At this point I have sanded the whole desk with 220 grit (you can still produce a scratch in the finish) and now I am wondering how to proceed ?

Give it another coat with the same paint and maybe put on a clear finish like
polycrylic? or
Sand down further, prime, repaint in laytex enamel .....

I have never used polycrylic and at $14+ a quart I want to make sure it will give me the hard surface that I want before I just "try" it to solve my problem. Anything else I should know about it before I try it?

Thanks for any help.

Given that you followed all the directions for applying the paint, I would consider that the can of paint is defective and return it for another from another lot.

Some colors of paint are difficult to use, dark green being on with which I have had many problems in obtaining a smooth finish. Latex paint is more durable than this experience you have had with your desk. Ordinarily, alkyd paint will produce a hard surface after 24 hours in proper conditions of temperature and humidity. Latex should cure for 4 - 7 days for maximum performance. In the long run, the performance of both paints is about the same.

Once you have another can of paint, sand the exisiting coats down to the point that the primer starts to show, and paint again.

Hope this helps.