As we know in the second Lord of the Rings movie, The Two Towers, Aragorn suggested to Theoden to ask Gondor for help. However Theoden was skeptical that Gondor will not come and didn't ask for help as he must be thinking Denethor will not help him. But Aragorn was heir of Isildur , he could have directly gone to Gondor and asked them to help by claiming his throne. Why didn't he do this?
I'll break down the events so you can see how this wouldn't be possible:
- Aragorn spots the marching Uruk Hai army on his return to Helms Deep
- Tells King Theoden that the army is approaching and will be there by nightfall
- Aragorn tell Theoden to send riders to Gondor to ask for their aid - Theoden refuses.
Aragorn has a choice:
- Ride for Gondor himself and risk missing the fight completely and returning to a ruined Helms Deep
- Stay, fight and hope Gandalf is good on his word.
Look to my coming at first light on the fifth day. At dawn, look to the east.
Even if he was willing to return to Gondor as a King at this point in his character arc (wasn't even close at this point in the films) He would never abandon Helms Deep and Rohan's women and children to potential slaughter.
If Theoden doesn't act and send out riders to call for aid... then there is nothing he can do.
I'm never convinced by questions like this as it is clearly not possible to give an answer on a character's motivations unless they are explicitly stated. That being said, if you watch the movies/read the books you cannot miss that Aragorn is not too keen on the idea of rocking up to Gondor and becoming a King. There are many sequences of events that lead to him changing his mind and this being possible - I think it is unrealistic to think that a random guy could show up to a city and claim to be the descendant of a king and everyone just go along with it.
Well for one, Denethor hates Aragorn big time, for being the favorite buudy of his dad, remember this was not the first time Aragorn helped Gondor during Ecthelion II rule(Denethor's father) Aragorn came to Gondor and served under Ecthelion using a different name and managed to make little Dany pretty jealous.
Gondor was not in its prime during the war of the ring, but it's not as cripled as it seemed in the movie, Gondor has all of its lands north of Anduin, Pelargir, Dol Amroth, Turnost, Linhir, Calembel and so on, so it was fully capable of sending a sizable force to help Rohan, The only reason Gondor had only 10,000 soldiers defending Minas Tirith during the siege and 200 Swan Knights was cose Denethor really lost his shit by the end there and did not mobilize the full might of the Gondor Army.
A lot of people say that Gondor had very small army during the war of the ring, but look at Aragorn after he becomes King of Gondor he oblitarates Harad and the Easterling and I am pretty sure that he didn't have to wait for a bunch of babies to be born razed and made into being soldiers so that he can have enough man power to invade Harad.
Also Gondor was not raided as much as it seems in the movie, middle earth learned that Sauron is back like 50-60 years ago so yeah Gondor was raided for similar amount of time, but otherwise when you check the history of Gondor Kings and Stewards the timeline usually goes like this - 200-300 years of peace that have 1- 2kings/ 3-4stewards that have nothing to be remembered for beside their names, then there is one or two huge Easterling/Haradrim/Orkish invasions under 1 king/steward then another 200-300 years peace, I am not saying that they didn't have a raids every no and then but it was not as crazy as some people state. Most of the time the Pirates of Umbar were not a problem as well since they were loyal citizens until, that one King that went crazy for this one northmen chick and their son was considered not a pure blood Dunedain king after his dad death, event that turned into the Gondorian Civil War and then you got Great Plage that kind of messed up thing as well.
Btw, sorry for the bad English guys, I am still learning the ropes, just how the hell to spell all of the words :)