Fine tuner spray only works if the pot is making a noise when you turn it.
Inside of the pot is a wiper which revolves around the rheostat - if the rheostat is broken - it might short out and cause a open circuit which would cause it not to attenuate.

http://www.discriminator.nl/handic0016/index-en.html

More then likely - the problem is internal or due to a lack of a proper antenna.

Radios by nature has a service life of about 7 years.
Things like capacitors and resistors loose their value with age.
Eventually they just wear out and has to be replaced.

If it was made in 2001 - its 11 years old.
Not to say that there is not scanners out there 40 years old that are still going strong, just to say that Radio Shack was never known for a high quality scanner.

Many times they bought someone else's brand such as Bearcat and just put their own face on it with a tag that said Radio Shack.

I highly doubt if there is any user serviceable parts - which could be repaired with no knowledge of electronics's or proper bench equipment.
Things such as a signal generator, a oscilloscope, and a schematic.