Its probably a good idea to contact Delta, their support is top notch, and they will probably have a good idea what might be wrong and will almost certainly be willing to help in some way.
http://www.delta-elektronika.nl/en/contact/company-details.html , the support address is the one you want.
Next to that you can of course start troubleshooting. Seeing as the current meter always displays 1.58A regardless of load, this would suggest an issue with the sensing circuitry, not the potentiometer etc.
The shape of the ripple is also weird, the converter should be switching at 100Khz, which is about the time between the ripples, but not quite. On my unit that ripple is sinusoidal, and also spot on 100Khz. Since the supply runs of a crystal timebase it should be pretty precise. Also the amplitude of the ripple is way to high.
But, the first rule of troubleshooting is "measure voltages", so start by checking the auxiliary supply that feeds the regulation circuitry. See if the voltages on the ribbon cable are ok, if they have lots of ripple etc. Those voltages are generated by a small flyback converter situated close by the main filter cap.
Also, don't forget to check the simple things, the pots inside the unit, the programming switches on the rear etc. There are also some things you can measure on the programming connector, There is an Imonitor output, see if that also thinks 1.58A is being measured by the shunt regardless of load. The reference voltage is also present there, see if that is within spec just to be sure
http://www.delta-elektronika.nl/upload/dts_es300.pdf you can find the pinout here.
All the ICs used are fairly standard types, so finding datasheets is no issue.