My car is broke down again and I'm a half of a month behind on rent. Could I take out a hardship withdrawl for my rent and use it to pay the rest of my rent and put a down payment down on a new car?

Yes, but it would be foolish to withdraw from your 401(k) for those purposes. What you will pay in interest and penalties will take a big chunk of your withdrawal.

The hardship withdrawal for rent is allowed only if it is to avoid imminent eviction. You may not use any of it on a down payment for a car. If you talk to your plan administrator I believe you will find that the check for the hardship withdrawal will be made out directly to your landlord to ensure that it's used for the stated purpose. You will also have to pay taxes and early distribution penalty on the amount of the withdrawal.

You can also talk to your plan administrator about taking a loan from your 401k savings. You can only take a certain percentage (usually half of what you have vested) and there is generally a processing fee (I have seen between $25 and $75) and then you pay interest on the loan. Repayment of the loan is generally conducted through deduction of your paycheck.
The Good: you can get the money to help with your needs, the interest you pay goes back into your account as you are borrowing from yourself.
The Bad: you are potentially missing profit on the money that in no longer in the account.

Disclaimer: I am no expert and in no way claim to be on any subject, this is only information I have obtained from my own personal experiences.