How can I tell if my hard drive is PATA or SATA?

To see the device description for the controller (assuming an internal (PCI) controller), which usually contains SATA for SATA controllers:

lspci -d $(cat /sys/block/sda/device/../../../vendor):$(cat /sys/block/sda/device/../../../device)

If you want to type less, just browsing the output of lspci is likely to give you the answer in a laptop (many desktop have both kinds of interfaces so you'd have to look up the drive you're interested in).

If that doesn't give you the answer, to see what driver is providing sda (you can then look up whether that driver is for a PATA or SATA controller):

readlink -f /sys/block/sda/device/../../../driver