We experimentally probe molecular ionization and dissociation of methane molecules in the gas phase upon their irradiation by intense pulses of white light that spans the wavelength range 500-850 nm. White light pulses are generated upon irradiation of BK7 glass by 36-fs-long pulses of intense 820 nm laser light. Comparison is made of the molecular fragmentation patterns obtained using white light that is depolarized with those obtained using single-color (820 nm) light that is highly chirped. On the basis of such comparison, we make hitherto-unavailable estimates of the in situ intensity of white light pulses. Results obtained using white light also indicate that resonances apparently do not play any role in the ionization dynamics that ensue upon irradiation by intense, broadband light; neither are the dynamics affected by the polarization properties of the 820 nm light that is used to generate the white light.