Game not letting me research top-level army techs?

[King]

Those silly Ruskies won't sell. I got relations to 198 or thereabouts, and yet they refuse to even give me Mariehamn for five techs and a big wad of cash. What they do want is me helping them in their war against the Ottoman Turks. Every time I refuse, relations go down by 10 or so. In short, I'm done speaking softly. Now I'm just waiting to get the Really Big Stick factory built (and building a formidable navy and first-rate railroad system, etc.).

Becuase that is a Russian core province. The AI does not like selling its cores.

 

[King]

I don't think it is. You're probably thinking of Viipuri (the one just Northwest of St. Petersburg), which is a core province for both Russia and Sweden (and Finland too, I suppose, should it get formed during the game).

Well check on the diplomacy map. The Russian Cores will have little dots on them.