Charles VII of France – disinherited by his own father in favour of Henry V (of England, for known reasons; not that he was supposed to become king in the first place since he had four older brothers), controlling really nothing of France, the parts he was supposed to control occupied by the English and Burgundians (like Paris and Reims), and reduced to control only of Bourges on the Loire river (hence referred to at the time as "the king of Bourges").
I think there are many rulers throughout history who were faced by awesome dilemmas when acending to power. Harold Godwinson of Saxon England immediately springs to mind, as does Baldwin IV of Outremer, William Prince of Orange in the 17th century and Robert Bruce of Scotland amongst many others.
However I think I am going to pluck for Alexius Kommenos I of the Eastern Roman (Byzantine) Empire. Alexius had an extremely difficult task when ascending the Imperial throne in 1081. The previous 100 hundred years had been an era of glory for the old Empire, seeing a renaissance in Byzantine fortunes both militarily, culturally and economic. Under the great Emperor Basil II known to history as the "Bulgar Slayer" great campaigns had been successfully undertaken. The frontier had been restored at the Danube and the Empires numerous enemies had either been vanquished or humbled. However, lacking a direct heir the years following Basil's death had seen many of his successes being slowly undone. This culminated during the reign of Romanos IV were due to court intrigues and outright treason on the battlefield saw the cream of the Byzantine army defeated at the battle of Manzikert in 1071. This defeat which is often overstated had great repercussions for the Empire which could have been nullified to an extent had the state not immediately plunged into a civil war.
By 1081 Alexius a prominent and capable general helped greatly by the intrigues and machinations of two women his mother "Anna Dalassene" and the Empress Maria of Alania whom between them actively orchestrated a political coup had somehow found himself elevated to the esteemed position of Alexius I Emperor of the Romans and God's Vice Garant on Earth.
This however would prove to be the easy part as Alexius now found himself as the ruler of an Empire which was broken, divided internally, bankrupt and beset on all sides by enemies who could smell the decay of a wounded giant and vyied to be the first to carve up choicest joints of the the carcass for themselves.
Alexius therefore had to set about the Herculean task of reuniting this once proud behemoth of an Empire containing 12 million souls and defending it from the ambitious and treacherous enemies both at home and on the frontiers. Feeling the weight of the legacy of not only nearly 800 years as Christendom's spirtual head but also millenia as ancient Greece and Rome's literal and spiritual successor Alexius set about his task.
That Alexius was mostly successfull in preserving the Empire and even regaining territory lost is an achievement that cannot be underestimated. Difficult choices and compromises had to be made in order to achieve this but they were born out of necessity and although some may criticise Alexius for perhaps instigating reforms that changed the Empire's traditional outlook and even perhaps sowed the seeds of its eventual fall? I would say that without Alexius the Empire would have fallen before 1100CE nevermind 1453 and had only his direct decendents though brave had been as prudent and tactful as Alexius then history may have been very different.