Did this work before you installed Windows 7 x64?
Things to try:
(1) I think you're describing a lead with one USB data connection and
one that only takes power from a USB port. Maybe you only need to re-
plug the data connector. They may be labelled "Data" and "Power".
(2) Use the disk drive with an externally powered or battery powered
hub, and switch it on first.
(3) If you have more than 2 USB ports, ports that are not next to each
other may be less likely to be sharing the port power supply.
(4) You might get away with plugging the power-connector into a port
on the laptop's charger, or into a separate battery with a USB port -
there are a few on the market.
(5) You could reboot the laptop more slowly, to give the external disk
more time to become ready. Press F8 to pause starting Windows, or
whichever key opens the boot device selector, or BIOS settings editor.
(6) Perhaps the d sk drive has an additional power port.
(7) You could get another external disk that only uses one USB port.