Im doing some painting in a rental that has been empty for a few weeks.  The landlord asked me to stick some new batteries in the hive and get the heating on to start getting the house warmed up.  
Ive never had one of these new tangled modern boilers so not sure what is supposed to happen with them.  Initially, it would fire up and then switch off again almost straight away.  Bled all the radiators and the 2 air vents above the cylinder.  It now fires up for a couple of minutes and then shuts down.  The radiators are getting warm, but it seems to be struggling to get all the rads hot.  Theres 2 tony ones and a towel rail upstairs and 2 medium size downstairs.  The living room and towel rail have lockshields both ends, the rest are all TRVs which are turned down fairly low.  It seems that as soon as a TRV opens, the downstairs rads all go cold.  
Is this likely to be an issue with the boiler itself?  Or more air stuck in a pipe somewhere?

Thanks in advance