The 300TDi normally starts straight away without any pre-heating regardless of the external temperature so if you are having this issue at this time of year (i.e. not cold yet) then yes, you have a problem.
You ask if it is the battery, is it turning over ok? If so then the battery is ok.
You should check the glow-plugs, make sure they are working (both the circuit and the plugs themselves) and if either is faulty then you may have found the problem but as I said, the 300TDi doesn't normally require any pre-heating anyway. Luckily checking the circuit is a simple electrical check and there is a pre-set timer-relay which also activates the light on the dash. Replacing a glow-plug is little more than replacing a spark-plug in a petrol engine, just take care and don't snap it if seized.
I had a glow-plug fail on me once (on my old 2.5NA D lump), took them all out and checked them on the bench and it was easy to see the faulty one, replaced them all though.