Blue screen and steady green status light.

probably drew moisture wherever it was stored.

I think that would be the digital video(formatter) board. Possible bad capacitor syndrome. Goog " bad caps and model."

This is just a shot - but it worked with my Sony (same problem).
Pressed remote power on button AND held Power button on TV on at the same time.

Set clicked 4 or 5 times and then came on....

Other, most have a (VERY small) reset switch on the rear - near where the power cord enters the TV... Use a flashlight and a mirror to locate it on your set....

not bulb component is damaged in power supply serction shutting down to protect other components

check the lamp

The green CRT's (color picutre tube or color wheel, or ballast) will need to be tested for replacement.
It is quite common with these tv's

You will need an ohmmeter and or voltmeter and test each component for currency and accuracy

If you hear a whining noise, the odds are it is the color wheel, the bearings are bad in it and will need to be replaced as a whole unit, kinda pricey, my suggestion, sale the bulb and all boards in it and which should fetch about 400+ and invest in a new TV, a color wheel is pricey unless you can find a deal

which caps did you replace? As the normal repair for the first generation dlp is to replace the (4) 1000 uf caps. the (2) 2200 uf caps and the (2) 3300uf caps on the power pwb when you get the 34 error code.

If no video and OSD is good then: Suspect the Signal PCB part # 930B923002

possible that over night your set took a power surge ,possible power supply fault.