The object PG 0043+039 has been identified as a broad absorption line (BAL) quasar based on its UV spectra. However, this optical luminous quasar has not been detected before in deep X-ray observations, making it the most extreme X-ray weak quasar known today. This study aims to detect PG 0043+039 in a deep X-ray exposure. The question is what causes the extreme X-ray weakness of PG 0043+039? Does PG 0043+039 show other spectral or continuum peculiarities? We took simultaneous deep X-ray spectra with XMM-Newton, far-ultraviolet (FUV) spectra with the Hubble Space Telescope (HST) and optical spectra of PG 0043+039 with the Hobby-Eberly Telescope (HET) and Southern African Large Telescope (SALT) in July, 2013. We have detected PG 0043+039 in our X-ray exposure taken in 2013. We presented our first results in a separate paper (Kollatschny et al. 2015). PG 0043+039 shows an extreme {\alpha}_ox gradient ({\alpha}_ox =-2.37). Furthermore, we were able to verify an X-ray flux of this source in a reanalysis of the X-ray data taken in 2005. At that time, it was fainter by a factor of 3.8 +- 0.9 with {\alpha}_ox=-2.55. The X-ray spectrum is compatible with a normal quasar power-law spectrum ({\Gamma}=1.70_-0.45^+0.57) with moderate intrinsic absorption (N_H=5.5_-3.9^+6.9 +- 10^21cm^-2) and reflection. The UV/optical flux of PG 0043+039 has increased by a factor of 1.8 compared to spectra taken in the years 1990-1991. The FUV spectrum is highly peculiar and dominated by broad bumps besides Ly{\alpha}. There is no detectable Lyman edge associated with the BAL absorbing gas seen in the CIV line. PG 0043+039 shows a maximum in the overall continuum flux at around {\lambda} 2500{\AA} in contrast to most other AGN where the maximum is found at shorter wavelengths. All the above is compatible with an intrinsically X-ray weak quasar, rather than an absorbed X-ray emission.