Hi,
When a single phase AC Motor such as in your tumble dryer won't self start but runs after being given a push start usually points to the starting capacitor. I do not know where this is located on the TV 630 but more than likely either nearby or actually on the motor frame. The capacitor will look like a tube with probably two push on connections. As this capacitor can hold quite a high electrical charge, make sure that the mains are isolated before fiddling with it. Also use insulated pliers if you are going to remove the push on connections.
A way to check the capacitor if it is of reasonable size (10 MicroFarad or more) is to briefly charge the capacitor with a 9 Volt battery, take care to observe polarity if the capacitor has the polarity symbols. After the brief charge test the voltage immediately using a multimeter or voltmeter. It should show a high voltage charge which will dissipate quite quickly with the meter leads attached. If the capacitor is faulty you can get a replacement from any electrical appliance repair shop. It does not have to be a HOOVER part as long as the capacity of the capacitor is the same or slightly more and the connections are compatible. Also the way it is secured into the machine will be a consideration. If you want to advise me of your results my email is richardd@horton.powernet.co.uk
Best of Luck
Richard Dunn
March 2008