Nichts

Ich weiß nicht was ich schreiben soll. I habe bin für die letzte Woche deprimiert gewesen.

1. Remember to always use "sein" as a helping verb with verbs of motion, change of state, to be and to become. 

2. "für" is never used with units of time. In this case, you don't need a prespotion, just like in English. "I was depressed last week." The two possible prespositions to use with units of time would be vor and seit. "Seit" is used when something started in the past and continues regularly into the present. "Ich spiele seit vielen Jahren Fußball." "vor" is used to mean "ago." "Ich bin vor vielen Wochen deprimiert gewesen." (but now I'm not) Remember that both "seit" and "vor" are dative prepositions and the unit of time after them needs to be in dative. (Hence, vielen).

Hope this helps.

For advice on what to write, read an article and discuss it here. Writing about what other people have written is very good practice for reading and writing.