From your screenshot it appears that the functions parX[t_] and parY[t_] returns a List
enclosing an expression in t. Not the "raw" expression itself. This does not work with ParametricPlot.
Compare:
ParametricPlot[{{Cos@t}, {Sin@t}}, {t, 0, 2 \[Pi]}]
Produces an empty plot
ParametricPlot[{Cos@t, Sin@t}, {t, 0, 2 \[Pi]}]
Plots a circle as expected
So, take away the enclosing curly brackets in the function definitions.