Do you mean a screen like this?:

If you using a RPi 3 B+, it may just be out of date firmware (see here) - you need to use newer image with the right firmware such as the offical Raspbian image - older and derivative images may still need to be updated for now (e.g. OctoPrint [1] [2] [3] )

Various troubleshooting methods can be found here:

With current firmware, a coloured splash screen (actually its just four pixels "blown up" by the GPU to full screen) is displayed after GPU firmware (start.elf) is loaded. This should be replaced by linux console a second later. However if the coloured screen remains, it suggests the kernel.img file is failing to boot. Try replacing it with a known good one.

Immediately after displaying the splash screen, the PI starts consuming a little more current. If the PI resets at that moment, it is an indication that the power supply isn't able to deliver the full current your PI requires, but dips its output voltage below a minimum when loaded with the full current the PI needs.

In some cases (Stuck on the Rainbow Screen), freezing at this point has been fixed by adding boot_delay=1 to the config.txt file. This can be done from a Windows PC, which should show several files in the FAT partition on your SD card including bootcode.bin, kernel.img, and config.txt. You can open config.txt in wordpad or any text editor. Add boot_delay=1 and save the file. Don't forget to 'eject' the card before removing it from the card reader. If you are reading the SD card from a working Pi, you can edit the file with sudo nano /boot/config.txt

Kernel Panic on boot

Text appears on screen, but then hangs with debug messages. This can be caused by USB devices such as keyboards. Try again with nothing in the USB.

Raspberry Pi shuts down (or restarts) soon after booting up

This is caused by a power supply producing too low a voltage. See Troubleshooting power problems

Pi boots sometimes but not always

With a known good power supply and known good SD card, the R-Pi boots occasionally, but other times shows only a tiny green flicker from the "OK" LED and it fails to start, even with no USB devices and no Ethernet. This has been reported several times_{[4] [5] [6]} and remains an open issue. Low voltage or an improper SD card can cause it. Some SD cards will work until they warm up slightly, and then fail_[7]. When exposed to 21 C room temperature the warmest part of an uncased working R-Pi should be 41 C_[8]. The wiki has a list of working SD cards. Buy from a reliable vendor as it has been claimed that 1/3 of all "Sandisk" labelled memory cards are counterfeit.

• It could be that the SD memory card is not making proper contact with the Raspberry Pi. Look at the SD card holder on the Raspberry Pi carefully. At first glance it may look fine, but the contacts must be springy and they must protrude at least 2mm as measured from the lower edge of the holder to the top of the contact bulge. Variations happen due to the solder process and the type of holder used. Some of the solder residue falls into the contact cavity, restricting the springiness and the height that the contact protrudes. You can fix this yourself, but remember you can void your warranty. The contacts are delicate, so be careful. Insert a needle pin under the contact bulge and pull lightly up until the one end of the contact unclips. Clean the cavity where the contact unclipped from any solder or other residue by blowing into the cavity. Clip the contact back into the cavity by lightly pushing it into the cavity. Do this for all the contacts. Refer to these photos: Media:SDcardHolder.JPG, Media:UnclipContact.JPG, Media:UnclippedContact.JPG

I would try other SD cards and power supplies, and check the Pi for defects, as well as different raspberry pi image. You may also want to try a different SD card reader, as some may format the card unreliably.