Those are common colloquial contractions.
「じゃ」=「では」 ← An extremely common contraction.
「てけない」=「ていけない」 ← The 「い」 in subsidiary verbs such as 「いく」 and 「いる」 is often omitted in informal speech.
Your translation is good.
Extra:
「[生]{い}きていく」 means "to go on living". 「生きていけない」 is the negative potential form of 「生きていく」. The affirmative potential form is 「生きていける」.
In all of these forms, the main verb is 「生きる」 and the subsidiary verb is 「いく」.
To connect a verb and a subsidiary verb, you need to first change the verb into its continuative form, then place 「て」 and finally place the subsidiary verb.
The continuative form of 「生きる」 is 「生き」, so you will get:
「生き + て + いく」(affirmative)
「生き + て + いけない」(negative)