Whether you hear anything on the short wave bands on your set (assuming it is working ok on these bands) depends on the type of antenna you are using and time of day – in general, the shorter wavelength bands (higher frequency) are more ‘lively’ in the daylight hours and the longer wavelength ones (lower frequency) during the evening/night-time. You should try to obtain a textbook that provides some info on shortwave propogation to gain a full understanding (look for old copies of the ARRL handbook etc or try ‘googling’ on teh web for things like ‘shortwave propogation’).
Of course you could have a problem in the set (very likley if you can hear nothing at all on all the shortwave bands). This could be due to many causes from the frequency converter tube being ‘tired’ and failing to oscillate at frequencies higher than the Broadcast Band (worth trying changing the tube for starters), followed by faulty components in the switched coils (eg, dirty switch contacts, broken coil winding) or poor alignment (is there evidence of someone ‘fiddling’ with the trimmers?). Have you checked the DC voltages around the tubes to see if they are ok/reasonable? (especially the frequency changer), as well as the AVC line (need a VTVM for this).
I have a JK-66 which has a set of pre-sets – these occasionally need cleaning or they stop working (not sure offhand if the JK-70 has this arrangement or not).