Well, here is a major bug that happens to all windows Vista and Windows 7 users.
You open the client but it won't run.
Fix: Right click the client and select "Run As Administrator"
Hope this helps to users who have this problem...
EDIT BY CRUCEO:
If the above does not work for ANY VERSIONS OF WINDOWS, you can solve your problem by manually registering the DLLs by following the steps provided. Just make sure you follow each step correctly and you will not have a problem nor harm your computer in any way.
Step 1. Navigate to your PokemonOnline installation directory, and then the Data folder (default: C:/Program Files/PokemonOnline/Data).
Step 2. Select all the files (CTRL+A) and copy them (CTRL+C).
Step 3. Navigate to your system32 directory (C:/Windows/system32).
Step 4. Paste all the files into the directory (CTRL+P).
NOTE: If a message asks you to overwrite a file, do NOT do it. Leave any existing files present alone as it could potentially harm your computer if it wasn't meant to be there!!!
By doing this you are manually registering those DLLs by adding them to the correct directory windows will search through to find the required library.