Dielectric relaxation measurements have been used to study the crossover in dynamics with temperature and pressure, onset of breakdown of the Debye-Stokes-Einstein law, and the relation between the alpha and the beta relaxations in diethyl phthalate. The measurements made over 10 decades in frequency and a broad range of temperature and pressure enable the dc conductivity and the alpha- and the beta-relaxations to be studied altogether. The isobaric data show that the alpha-relaxation time tau(alpha) has temperature dependence that crosses over from one Vogel-Fulcher-Tammann-Hesse form to another at T(B) approximately 227 K and tau(alpha) approximately 10(-2) s. The dc conductivity sigma exhibits similar crossover at the same T(B). At temperatures above T(B), tau(alpha) and sigma have the same temperature dependence, but below T(B) they become different and the Debye-Stokes-Einstein law breaks down. The breadth of the alpha relaxation is nearly constant for T<T(B), but decreases with increasing temperature for T>T(B). The time dependence of tau(beta) is Arrhenius, which when extrapolated to higher temperatures intersects tau(alpha) at T(beta) nearly coincident with T(B). Isothermal measurements at various applied pressures when compared with isobaric data show that the shape of the alpha-relaxation depends only on tau(alpha), and not on the T and P combinations. At a constant temperature, while tau(alpha) increases rapidly with pressure, the beta-relaxation time tau(beta) is insensitive to applied pressure. This behavior is exactly the same as found in 1,1(')-bis (p-methoxyphenyl) cyclohexane. The findings are discussed in the framework of the coupling model.