She has no experience with a typewriter, and no skills of that sort either.

Literal

She [topic-は] typewriter [genitive-の] experience [topic-は] not-exist [and-し], that-kind-of skills [also-も] not-exist.

~し is the listing connector that strings together reasons or parallel facts — 'X and (also) Y, ...' — often with the implication that the speaker is piling up evidence. Here it links two negative claims: no experience, and no skills. The two は's (経験は, contrasted topic) and the も on 技術 ('also'/'either' under negation) coordinate with each other to make the parallelism feel intentional: 'as for experience, none — and also no skills of that kind.' そういう ('that kind of, that sort of') refers anaphorically to a category implied by 'typewriter'-related work, gesturing at office skills broadly without naming them. Today タイプライター is a bit of a period word — typewriters fell out of office use in Japan during the 1980s–90s, replaced first by 和文タイプ word processors and then by computers.