More than likely it just needs a new battery. If the power is sagging (called a brownout) the UPS is trying to switch over to the battery to keep the power consistent. The beeping is probably a code that indicates there is an issue with low voltage on the battery. New batteries are around $20-25. Here's a link to the replacement battery: http://batteryinternational.com/apc-backups-es-be350es-ups-battery-ups-batteries-f1.html

Hope that helps.