Four dense cores, L1582A, L1689A, B133 and B68, classified as prestellar in terms of the absence of detectable NIR emission, are observed at radio wavelengths to investigate whether they nurture very young protostars. No definite young protostars were discovered in any of the four cores observed. A few radio sources were discovered close to the observed cores, but these are most likely extragalactic sources or YSOs unrelated to the cores observed. In L1582A we discovered a weak radio source near the centre of the core with radio characteristics and offset from the peak of the submillimeter emission similar to that of the newly discovered protostar in the core L1014, indicating a possible protostellar nature for this source. This needs to be confirmed with near- and/or mid-infrared observations (e.g. with Spitzer). Hence based on the current observations we are unable to confirm unequivocally that L1582A is starless. In L1689A a possible 4.5-sigma radio source was discovered at the centre of the core, but needs to be confirmed with future observations. In B133 a weak radio source, possibly a protostar, was discovered at the edge of the core on a local peak of the core submm emission, but no source was detected at the centre of the core. Thus, B133 is probably starless, but may have a protostar at its edge. In B68 no radio sources were discovered inside or at the edge of the core, and thus B68 is indeed starless. Four more radio sources with spectral indices characteristic of young protostars were discovered outside the cores but within the extended clouds in which these cores reside. Conclusions: We conclude that the number of cores misclassified as prestellar is probably very small and does not significantly alter the estimated lifetime of the prestellar phase.Read less <