Eighteen 280mm guns vs. six 15". If the Germans are serious about a fight and the weather negates the DD's and the Germans know its just Renown (they though there was another capital ship or at least a heavy cruiser) then I don't give Renown much chance at all. At the range in question Renown can't defeat the Twins citadel protection. You need a weird deflection (like north cape) to get a shell into the engineering spaces. As such the Twins should be able to avoid flooding of the engineering spaces and have full power; assuming the engines don't break down which one did break down here. Flooding of bow & stern spaces is very possible but to say it would be enough to slow the ships / doom them is a very large assumption.
Keep in mind N square. Renown because she is facing more firepower is going to loose her own combat power quicker and quicker as the combat advantage shifts more and more towards the Germans.
Michael
On a one against two base, the Germans are in an advantage, as they can force the single British ship to split her already modest number of heavy guns on two targets, while the two German battleships can both bring on their whole armament normally. The British also had a disatvatage in speed, as the HSM Renown after her refit was just good for a maximum of 29 knots in fair wheather and certainly less in the heavy seas encountered, when in the OTL engaging Scharnhorst and Gneisenau. The two German battleship both could make 32 knots in fair wheather and had generally better lines and higher freeboard compared to the basically unaltered hulllines of HMS Renowns, which included a very low stern which tended to dig in at high speed.
The advantage in speed of around some 5 knots in the sort of wheather encountered was possibly a serious advantage for the germans, combined with their generally tougher protective systems and more numereous heavy guns, dispite them being smaller. The Germans could choose to engage and disengage at will against one target, if they knew HMS Renown was just alone out there (discounting the Destroyers). The Germans however expected correctly that both HMS Repulse and HMS Warspite were in the same general erea as well, as earlier scoutreports had confirmed the presence of these two ships as wel, although not precisely where. (HMS Repulse was patrolling of the Narvik erea, with her Destroyerscreen, while HMS Warspite was still in the region as well, acting as flagship of the Homefleet at the time. Further the 1st cruisers squadron of four heavy cruisers was known to have set sail for Norwegian waters earlier that week and was not reported yet about.
So the Germans had a lot of guessing to do, as they at the time lacked a reliable radar yet and other intelligence was also far from accurate.