Usually when there are problems with booting roms on the r4 it is because the kernel is out of date. Download the latest kernel for your r4 at http://www.r4ds.com/download-en.htm
If the games still don't work, you might need to replace the arm7.bin file in the game. To do this, you will need to use a program called DSLazy. You can download it here
. So to replace the arm7.bin, you will need a nds rom that works without the arm7.bin fix.
Step One: Start DSLazy.
Step Two: Browse for the file that works without the fix (I use Tetris DS)
Step Three: Click Unpack. This will create a new folder called NDS_UNPACK
Step Four: Move the arm7.bin inside the new folder somewhere safe. Close DSLazy
Step Five: Complete steps 1-3 again.
Step Six: Now open NDS_UNPACK that you just created with the game you want to fix and put the arm7.bin that you moved from step four into the NDS_UNPACK to replace the one already in there with the new one.
Step Seven: Click NDS Packer in DSLazy. This will create a new version of the game you want to fix with a new arm7.bin
Step Eight: You are done. Copy the game to your r4 and load it. The game should work.
If this didn't work, which shouldn't happen, try re-downloading your roms.
If it STILL doesn't work, there might be a problem with your r4, and you might want to get it fixed or get a new one.
~hope this helps.