Basic approach will be to pick a line and get its slope, call it m.

Then select all lines/polylines in the drawing and iterate through them. You'll probably want to filter out for polylines that only have 2 vertices.

check the slope of each line, call it m2

if((m2.isclose(m)) or (m2.isclose(m+PI))) then the line/polyline is parallel if it's parallel, highlight it.

You can also find the slope of a line by getting the (change in Y)/(change in X) between the endpoints.

Edit: You'll also need to check for a vertical line, which has an undefined slope (change in x = 0).

Not sure what language you're hoping to work in, but that's the basic idea. I've no idea how to do this without code.