The dvd player in my 2005 dodge grand caravan will not work or stop blinking. It blinks continually when the care is running

That is typically a sign that it has failed the self test & is most likely going to need to be removed & sent to be repaired or replace it.
Sorry to be the bearer of bad news. :(

I am sure if you use your hand it will go off? In that case your headlight combination switch is going bad,

You have but one choice remove the player and have it repaired by an approved factory repair center.

Call around to Best Buy the install DVD players and offer all kinds of pricing

is the check engine light blinking? if so have it tested for codes, Kragen auto and others do this test for free, just ask for a OBD2 fault code test. let me know the results and we can work from there.

Bad bulb. When a turn signal bulb blows the other bulb on the same side will blink twice as fast since there is only half the load on the circuit. If the engine light came on at the same time the bulb blew then it probably meant that the computer notice the drop in resistance in the circuit and came on to let you know something is wrong. Change the bulb and have the engine code scanned/cleared. Autozone will scan and clear the code for free, except in Ca.

The procedure for re-setting the HVAC control panel on a 1998 Dodge Grand Caravan follows:
With ignition on but not running
1. turn knob to air vents
2. turn fan knob to ON
3. temperature setting on COLD (2X) {I have dual temp controls}
4. hold top(rear wiper) and bottom (rear wiper with wash) buttons pressing down together until all the buttons cycle through (this will require 1 to 2 minutes of continuous pressing)
I learned this from a very helpful local Dodge service adviser

disconnect battery pump the break 3 to 5 times wait 5 minutes reconnect battery and it should eject.

you need to take it apart and clean it or send a disk in that cleans the inside.