Michael, i found the solution. As Rich R. mentioned it was issue with sertificates.
A. You will require second computer with working well dropbox. My second PC was with win81.
B. When i did it on first pc (with windows xp), it was date set 2013-07-18. But i believe it optional.
So following this article https://support.microsoft.com/en-us/kb/916260 ,
you will need:
-----------------------
RESOLUTION
To resolve this problem, follow these steps:
Export certificates from a computer that is not experiencing this problem. To do this, follow these steps:
Start Microsoft Internet Explorer.
On the Tools menu, click Internet Options.
Click the Content tab, and then click Certificates.
Click the Trusted Root Certification Authorities tab.
Select all the certificates in the store. To do this, click the first certificate in the store, and then hold down the SHIFT key as you scroll down the list to the last certificate in the store.
Click Export, and then click Next to start the Certificate Export Wizard.
Click Browse to select a location to save the file, and then click Next.
Note Save the file in the default .p7b format. Use a naming convention that represents the store.
Click Finish, and then click OK when the export is successful.
Repeat steps 1d through 1h for the Intermediate Certification Authorities store.
Move the .p7b file that you saved in step 1 to the computer that is experiencing the problem.
Import the certificates to the computer that is experiencing the problem. To do this, follow these steps:
Start Internet Explorer.
On the Tools menu, click Internet Options.
Click the Content tab, and then click Certificates.
Click Import, and then click Next to start the Certificate Import Wizard.
Click Browse to select the location of the file that you saved in step 1, and then click Next
Click Browse, click Trusted Root Certification Authorities, click OK, and then click Next.
Click Finish, and then click OK after the import succeeds.
Repeat steps 3d through 3g for the Intermediate Certification Authorities store.
-----------------------
After these steps the dropbox on windows xp was updated and started to sync as previous.
