H3NRY mentions power supplies. SEs came with either an Astec or Sony power supply. As with the IIcx and IIci, which can also have a GE, the Astec is the inferior of the two, having issues both when the machines were new and especially today. I have not encountered a fully functional Astec power supply in 15 years. They weren't as common as the Sony, so this could be one reason, but the reliability is a huge factor as well. Even the Macintosh Bible, Fourth Edition cautioned against purchasing a used SE with an Astec supply. I'd rate them in the same category as the original beige-switched 128K/512K/Plus power supplies in terms of reliability.

There's an easy way to tell the difference between the two brands. The rocker switch on an Astec is white, while Sonys sport a black switch.

If you are lucky enough to have a working Astec supply, be warned about problems with voltages drifting (as H3NRY indicated). If you happen to have an extra power brick, you may want to swap it just to rule another component out. The SE, SE SuperDrive/FDHD, and SE/30 all use the same power supply type.