She kept the old newspapers in a stack.

Literal

She [topic-は] old-newspapers [object-を] heap [into-に] do-and had-set-aside.

Two state-changing patterns chained together. 山積みにする ('to make into a heap') uses the resultative ~にする — the pattern that turns a noun phrase into the new state of an object, the same shape as 部屋をきれいにする ('make the room clean'). Then 置いておいた combines the て-form of 置く ('to place') with the auxiliary ~ておく ('do in advance / leave in a useful state'), so the whole verb chain reads 'set them down and left them that way.' Old newspapers traditionally pile up at home for 古紙回収 (paper-recycling pickup), bundled with twine and set out on designated days — sometimes collected by neighborhood groups or scout troops in exchange for tissue paper.