Re-install WordPress, then add the following line inside your template's <body> tags:
<!-- wpscanner -->
Once that's done, run the web-based BlogSecurify scanner at http://www.blogsecurify.com/ , and post any security warnings (WITHOUT the address/URL to your blog) it gives you back in this thread so we can make suggestions.
After running the BlogSecurify scanner, MAKE SURE you remove the <!-- wpscanner --> line from your template , as this will prevent others from running the scanner on your site and obtaining any vulnerability information.
You might also consider installing the WordPress Security Scan plug-in, which will tell you what permissions should be set on several crucial WordPress files.
If you're not familiar with setting write permissions, download the Filezilla FTP client and use it to correctly set the file permissions on your site.
Hope we can help you out! :-)