Could a frayed wire have damaged my computer?

My mac charger broke, the wires were exposed… My husband thought he could fix it himself. So he did something to it, involving electrical tape and what not. It worked and I was happy. Well now, three weeks later, there are issues. It seems to charge the computer fine, but as soon as I unplug it, the computer shuts down. I am able to turn it back on after a few seconds, with or without being plugged in. The only really wonky thing with my computer is that it seems to reset the date to the year 2000 when it turns back on, just for a few seconds, until it connects to wifi and realizes what year we are in.

I have an appointment with Apple, but can't get there until the weekend. My question is, should I just stop using this charger and accept not being able to use my computer for the rest of the week? I don't want to cause further damage, but I'm not sure if this is just a charger issue and I can make do with it until then?