Как-то раз, заходя на компьютер, я случайно наткнулась на один из отчетов Клиффа для штаб-квартиры Церкви.
Original: One day, when I was logging onto my computer, I accidentally came across one of Cliff's reports to Church headquarters.

What the hell is that? Looks like inaccurate translation in bad Russian. Where is "my"?

The correct variant: "Как-то раз, зайдя в свой компьютер, я случайно наткнулась..."
"Зайдя" (or "войдя") because perfective is preferable, the author didn't mean a login process, it's obvious from the context.