If you have an eSATA port built in, it is VERY likely that its connector is on the back or side of your case. Look up its appearance and look around where all the other connectors are for it. You could also check the manual for that model.
If you don't have that, I really doubt you would have any way to use an adapter to connect to an internal regular SATA port. But you could get a PCMCIA card to provide eSATA ports, like these: