Pesuke Dezimra Part One (Hodu until Lamnatzeah)
Pesuke Dezimra Part Two (Baruch Sheamar until Yishtabah)
This recording was sung fast because it was meant for weekday reading. Nevertheless, I did sing Hashem Melech, Baruch Sheamar and Yishtabah.
The chapters of Tehilim beginning with Ashre followed by the Haleluyahs are also recited quickly and Be'ezrat Hashem, I will have them recorded more slowly in the near future. In the meantime you can just slow down the playback on YouTube.
I must note that most synagogues don't sing Hashem Melech, Baruch Sheamar and Yishtabah on a regular weekday unless there is some sort of simha in the synagogue. Usually, it is just read.