A question for you GIS gurus out there

I am trying to parse ESRI shapefiles that describe FAA TFRs. But they
are in NAD83 projections, with accompanying .prj files that look like
this:

PROJCS["North_America_Lambert_Conformal_Conic",
GEOGCS["GCS_North_American_1983",
DATUM["D_North_American_1983",SPHEROID["GRS_1980",
6378137.0,298.257222101]],
PRIMEM["Greenwich",0.0],UNIT["Degree",0.0174532925199433]],
PROJECTION["Lambert_Conformal_Conic"],
PARAMETER["False_Easting",0.0],
PARAMETER["False_Northing",0.0],
PARAMETER["Central_Meridian",-93.13333333333335],
PARAMETER["Standard_Parallel_1",47.41333914430852],
PARAMETER["Standard_Parallel_2",47.43554955001912],
PARAMETER["Latitude_Of_Origin",40.0],UNIT["Meter",1.0]
]

A partial text dump of the corresponding .shp file looks like this:

Shape:8 (Polygon) nVertices=37, nParts=1
Bounds-3703.999933,823435.273920, 0, 0)
to ( 3703.999933,830843.274058, 0, 0)
( 0.00000000,830843.27405814, 0, 0) Ring
(643.19289130,830787.00193647, 0, 0)
(1266.84264658,830619.89536055, 0, 0)
(1852.00012149,830347.03211620, 0, 0)
(2380.88541892,829976.70258255, 0, 0)
...

I have not been able to figure out how to use .prj parameters to
transform the coordinates in the shapefiles to WGS84 (lat/lon) format.
Seems to me it should be a rather simple formula. Anyone out there
familiar with this problem?

-ted/2NO