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Having followed the Nauka's issues for the past 20-odd years (sorry - ad coming: http://www.www.russianspaceweb.com/ - not affiliated, but have paid for access & lots of other reading) the reporting by ElReg is very good and seems accurate as far as I can tell. (Well done - tricky topic!) They have a contingency (which involves docking with the ISS) that if the main engine completely fails then they can still proceed with the manoeuvring engines (DPK), but will be much slower. It seems that a software error (oh Spaghetti Monster, how we programmers fail!) caused the premature pressurisation of the propellant tanks which has meant that the over-pressure (not dangerous) has meant they cannot use the main engine (at the moment). This explains the wild pressure readings received regarding the tank pressure. They seem convinced there is no leak. They are performing a test burn early this evening and if that succeeds then they can progress & move to a higher orbit to plan the much slower rendezvous with the ISS. There is apparently enough fuel for two docking attempts (though how much for rendezvous I do not know). The main issue is to get it to a higher orbit I think. Sadly due to the previous contamination of the tanks, refuelling the Nauke is probably off the cards, so sending a Progress to refuel it is most unlikely.

But sending an unmanned Progress, or unmanned Soyuz (recall they can both be controlled remotely, from the ISS or ground) to provide extra propulsion might work, if they can a) stabilise the orbit of Nauka and b) send one up in time. (They may not have a "hot spare" and want about the launcher - that too. The crash programmes of the 60s are long gone. I'd imagine to launch such an rescue would take about 3-4 days if they had everything at hand and worked 24hrs a day in multiple shifts (not unknown) as finessing, placing on the pad & fuelling of either takes time... By which time the Nauka would have long since burnt up: recall 30 orbits at about 2hrs per orbit is 60hrs. The clock is ticking and they are under the hammer (and possibly sickle!)......