It is neither "all the things" nor "(just) one thing".
The question is not specific about the amount of information asked so should be understood to mean "what noteworthy thing(s) did you do last week on the computer?".
La semaine dernière always means "last calendar week", never the previous seven days just like l'année dernière means 2017 if we are in 2018, not the last 365 days1.
La semaine dernière doesn't mean "one week ago" although "one week ago" necessarily occurred la semaine dernière. La semaine dernière can mean anything between "any time belonging to the previous calendar week" and "during the whole previous week".
Note also that semaine is often only a period of five days, Monday to Friday, the whole week being the concatenation of semaine and week-end. Unlike in the US and many countries, Sunday is generally considered the last day of the week in France.
Tell me one thing you did one week ago on the computer.
would translate to:
Dis-moi une chose que tu as faite sur l'ordinateur il y a une semaine.
List all of the things you have done within the last week on the computer.
Dis-moi (or fait-moi la liste de) tout ce que tu as fait sur l'ordinateur (durant / au cours de) la semaine dernière.
If you ask about the current ending week, not the previous one, you might ask:
Dis-moi tout ce que tu as fait sur l'ordinateur cette semaine.
1One exception is when referring to schools/universities where the year, noted for example 2018-2019, starts in September and ends in June or early July