I have a new eyecon model001 that does not take pictures after dark. have another trail camera next to it and it works fine.

Was it always like that or just happened. It it start happening now, indicates that there is battery or capacitor on board to keep real time clock going. It is also possible that you only have a short period of time to replace battery 30 sec, 1 min maybe. Try by setting time, removing and putting back batteries.

Get it serviced ?

Try Ebay or the manufacturer. You'll need the make, model and part number to order it.

In Nikon, some things can avoid taking a picture. This can be set in the menu's. One blocking taking pictures, is no card in the camera. Another one ca be the camera can't focus and does not allow you to take a picture. Or the scene is to dark.
When the camera is in Autmatic, and a working memory card is installed every thing should work fine. Let me know how you go on.

Turn camera off take out battery's and sd card. Once everything is out put it to the on postion for about 2-3 min. Then put battery's back in with the camera being on still leave sd card out. Once it says no card turn camera off then put sd card back test in dark. If still not working call Moultire 8006533334 option 1 and 1 for a live person.

Bad camera, try have them replace it,or fix it for you.

Try doing a hard reset, Turn camera off remove battery's and sd card. With everything out. Push on/off for about 5 sec. Put good battery's in ig. If you using cheap battery's make sure your are using Duracell or Engerzier battery's not rechargeable. Also make sure not using a micro sd card and nothing higher than a class 4 which is the speed of the card not the size. If still need help call with equipment to troubleshoot to Moultire 800653334 option 1 and 1 for a live person.

you need to replace the lcd, has a look here.

Does the flash work? Could be flash circuit or day/night sensor.If you have another D40/D50 camera that flash works but has other problems,swap out the sensors.If not the sensor but the flash circuit then most likely one of the large charge capacitors which has to be soldered in.I use a digital multimeter with I/O capacitor test function..these caps should be about 250mfd.