Context. A 10-arcmin region around the Hubble Deep Field (North) contains 92 radio sources brighter than 40 µJy which are wellresolved by MERLIN+VLA at 0. 2−2 resolution (average size ∼1 ). 55 of these have Chandra X-ray counterparts in the 2-Ms CDF(N) field including at least 17 with a hard X-ray photon index and high luminosity characteristic of a type-II (obscured) AGN. More than 70% of the radio sources have been classified as starbursts or AGN using radio morphologies, spectral indices and comparisons with optical appearance and rest-frame MIR emission. On this basis, starbursts outnumber radio AGN 3:1. Aims. We investigate the possibility that very luminous radio and X-ray emission originates from different phenomena in the same high-redshift galaxies. Methods. This study extends the Virtual Observatory (VO) methods previously used to identify X-ray-selected obscured type-II AGN, to examine the relationship between radio and X-ray emission. We describe a VO cut-out server for MERLIN+VLA 1.4-GHz radio images in the HDF(N) region. Results. The high-redshift starbursts have typical sizes of 5-10 kpc and star formation rates of ∼1000 M yr −1 , an order of magnitude more extended and intense than in the local universe. There is no obvious correlation between radio and X-ray luminosities nor spectral indices at z > ∼ 1.3. About 70% of both the radio-selected AGN and the starburst samples were detected by Chandra. The X-ray luminosity indicates the presence of an AGN in at least half of the 45 cross-matched radio starbursts. Eleven of these are type-II AGN, of which 7 are at z ≥ 1.5. This distribution overlaps closely with the X-ray detected radio sources which were also detected by SCUBA. In contrast, all but one of the AGN-dominated radio sources are at z < 1.5, including the 4 which are also X-ray selected type-II AGN. The stacked 1.4-GHz emission at the positions of radio-faint X-ray sources is correlated with X-ray hardness. Conclusions. Almost all extended radio starbursts at z > 1.3 host X-ray selected obscured AGN. The radio emission from most of these ultra-luminous objects is dominated by star formation although the highest redshift (z = 4.424) source has a substantial AGN contribution. Star-formation appears to contribute less than 1/3 of their X-ray luminosity. Our results support the inferences from SCUBA and IR data, that at z > ∼ 1.5, star formation is observably more extended and more copious, it is closely linked to AGN activity and it is triggered differently, compared with star formation at lower redshifts.