Be very careful with how you interpret this molecule. Although the 1H NMR spectrum appears as a single line, this is actually an AA'A''A''' system, meaning that, although chemically equivalent, all four protons are magnetically non-equivalent, but have coincidental chemical shift. The coupling between all protons is different; JA-A''' is different to JA-A''' is different to JA'-A'' is different to JA'-A''' and so on.
So yes, the spectrum is as you thought. p-dichlorobenzene IS a single peak in the 1H NMR spectrum.
Below is a set of simulations for a generic para disubstituted benzene system, which is an AA'BB' system. A is chemically equivalent to A', but magnetically non-equivalent. A is chemically AND magnetically non-equivalent to B. Your system is just a special case example of these types of systems, with all protons being chemically equivalent, but magnetically non-equivalent. These are second order systems, which have a lot of complex additional splitting structure in their spectrum. Like all spin systems, as the chemical shift difference becomes less (the peaks move closer together), the tilting, (or tenting or roofing, depending on which text book you read) becomes more pronounced, and the wings on the main peaks become smaller and smaller. Eventually, they collapse into a single peak at very small chemical shift difference.
The fine text which you can't read (sorry about that), gives the coupling constants for the system, which are bog-standard ortho/meta/para couplings: Jortho=7Hz, Jmeta=3Hz; Jpara=1Hz. The only variable in the simulations is the chemical shift of the downfield peak, which slowly moves towards its upfield partner.