Panel seems fried. If you disconnect and reconnect to power with no response, its dead. Without the panel, those sensors have nothing to communicate with. It's either replace the panel, or replace the whole system.
For what you want, simplisafe or something sounds perfect. You don't even have to pay the monthly subscription to use the sensors or alarm.
Edit: Found a replacement panel on ebay, no guarantee you can provision the sensors to it yourself though. https://www.ebay.com/itm/125616888699?mkcid=16&mkevt=1&mkrid=711-127632-2357-0&ssspo=l1iaPyWwQFO&sssrc=4429486&ssuid=EXVRJ8MXR4O&var=&widget_ver=artemis&media=COPY
simplisafe