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She couldn't bring herself to pick up a heavy, demanding book.
Literal
She [topic-は] shoulders [subject-が] stiffen book [object-を] read mood [target-に][contrast-は] could-not-become.
The phrase 肩が凝る has a delightful double life. Literally it means 'shoulders stiffen,' a chronic Japanese complaint and a frequent excuse for visiting a 整体 ('manual therapist'). Idiomatically — and this is the sense triggered when 肩が凝る attaches as a pre-noun modifier — it means 'serious, sober, demanding, the kind of thing that makes your shoulders tense up.' So 肩が凝る本 is 'a stuffy / heavy / intellectually demanding book.' On top of that, ~気になる/なれる builds the 'feel like / be in the mood to' construction; the は inside 気には is contrastive — 'as for that mood, it didn't come.' The whole sentence: 'she just couldn't summon the energy for that kind of book.'