。
She's thinking of getting married but can't make up her mind.
Literal
She [topic-は] marry-let-us [thinking-と思う] [but-が] resolution [subject-が] doesn't-attach.
Two grammar patterns sit side by side. ~(よ)うと思う uses the volitional ~(よ)う ('let me / let's') quoted with と and embedded in 思う to report one's own intention or plan: '(I'm) thinking I'll do X.' The negative or hesitant counterpart: 決心がつく / つかない ('one's resolve forms / doesn't form') — an idiom in which 決心 ('resolution, determination') is treated as something that 'sticks' or doesn't, with つく ('to attach, settle') as its intransitive verb. The mid-sentence が is the soft 'but' connector, marking the stalemate between intention and action.