Suddenly this error appeared: “A problem is preventing Window from accurately checking the license for this computer. Error Code : 0×80090006″.

I have no idea why.

According to others what you can do one the followin:

• Log into safe mode and re-register a couple of dlls:
  regsvr32 regwizc.dll
  regsvr32 licdll.dll
• Fix C drive association by using regedit32:
  See KB914232
• Reinstall or repair.

For only the third worked.

You can backup files by using Safe mode.

Remember,  backup your data often.

Later edit:

You should verify your XP license or for viruses/rootkits or, more general, malware.
You can see here how much increased the number of searches for 0×80090006 in February: Link to google insight.