Can I get money back for a computer that isn't working even after the warranty is up if the problem started before it expired?

Most likely you will not be able to get your computer repaired for free or a partial refund since the problem with it arose before the warranty was up but you apparently did not advise the seller, distributor and/or its manufacture of the problem.

Had you done so, you might have been able to get the problem repaired for free or possibly a new computer. It is important in such a situation to give written notice under the warranty of the problem. You could possibly write and advise the company about the problem and see what happens. However, I would not be too optimistic that you will receive a favorable response to your request.