I am not an expert at germinating. I would leaving it alone in its current soil and make sure its gets some sun - not just "light". Without sun it will die fast. Once its first sprout has some sun it will begin establishing and can be repotted a month later.

Don't leave it near the t.v., since the radiation will not be good for it. That is why pet shops tell people not to put an aquarium or terrarium near a t.v. Also move it outside to get as much sunlight as possible, if it is not cold where you live. As a sprout don't let it be exposed to any temps below about 40F, and your days should be in the 60's or warmer. Don't repot it for a few months after the first green shoot has emerged from the soil, then very carefully repot it into a good organic potting soil that has some sand, since date palms are desert palms and don't like to be too wet. When you do repot it, repot it at the same depth it was growing in in the other container. Watering it about 3 times per week in warmer weather and only once a week in cooler weather should be plenty. When they are full grown, they are hardy down to about 18F, which means they can survive the warmer parts of a Zone 8B Climate.

John

I would not worry about the orientation, upside down or what ever. Seeds and seedlings have a wonderful way of working that out all by them selves. It will do just fine.