It could be a number of things. First replace the battery.
Disconnect everything except the mouse and keyboard. Turn on the Mac Plus and you should hear the start up chime and see the flashing question mark. If you get the sad mac face then you have a RAM/motherboard/analog board issue to figure out.
At this point I would pull the RAM SIMMS, clean the edges with a soft eraser and reset them. Reassemble and try again.
http://lowendmac.com/ram/plus.shtml
If you get the sad mac, pull the SIMMS out of Bank B (leaving 2 in Bank A) and try again (it will boot with two 256K SIMMS, 512K total).
If that doesn't help then you have to get a pair of RAM SIMMS that are known to be good.
My guess is that the RAM has come loose and a re-seat might just do the trick.
You should upgrade the Plus to 4 MB as memory is so cheap.