We present here a new spectral energy distribution ( SED ) fitting approach that we adopt to select radio-excess sources amongst distant star-forming galaxies in the GOODS- Herschel ( North ) field and to reveal the presence of hidden , highly obscured AGN . Through extensive SED analysis of 458 galaxies with radio 1.4 GHz and mid-IR 24 \mu m detections using some of the deepest Chandra X-ray , Spitzer and Herschel infrared , and VLA radio data available to date , we have robustly identified a sample of 51 radio-excess AGN ( \sim 1300 deg ^ { -2 } ) out to redshift z \approx 3 . These radio-excess AGN have a significantly lower far-IR/radio ratio ( q < 1.68 , 3 \sigma ) than the typical relation observed for star-forming galaxies ( q \approx 2.2 ) . We find that \approx 45 % of these radio-excess sources have a dominant AGN component in the mid-IR band , while for the remainders the excess radio emission is the only indicator of AGN activity . The presence of an AGN is also confirmed by the detection of a compact radio core in deep VLBI 1.4 GHz observations for eight of our radio-excess sources ( \approx 16 % ; \approx 66 % of the VLBI detected sources in this field ) , with the excess radio flux measured from our SED analysis agreeing , to within a factor of two , with the radio core emission measured by VLBI . We find that the fraction of radio-excess AGN increases with X-ray luminosity reaching \sim 60 % at L _ { X } \approx 10 ^ { 44 } -10 ^ { 45 } erg s ^ { -1 } , making these sources an important part of the total AGN population . However , almost half ( 24/51 ) of these radio-excess AGN are not detected in the deep Chandra X-ray data , suggesting that some of these sources might be heavily obscured . Amongst the radio-excess AGN we can distinguish three groups of objects : i ) AGN clearly identified in infrared ( and often in X-rays ) , a fraction of which are likely to be distant Compton-thick AGN , ii ) moderate luminosity AGN ( L _ { X } \lesssim 10 ^ { 43 } erg s ^ { -1 } ) hosted in strong star-forming galaxies , and iii ) a small fraction of low accretion-rate AGN hosted in passive ( i.e . weak or no star-forming ) galaxies . We also find that the specific star formation rates ( sSFRs ) of the radio-excess AGN are on average lower that those observed for X-ray selected AGN hosts , indicating that our sources are forming stars more slowly than typical AGN hosts , and possibly their star formation is progressively quenching .