I have read the forum for using DTDonate with SSL. I have gotten a shared SSL with my clients hosting provider (HostMySite, as an aside never host with these people, what a nightmare). I have made the link to the DTDonate URL with the HTTPS URL that HostMySite gave me to use. However when I click that link I get the alert message displayed in the attacment below, I have to click about 50 times, the site finally displays sans all CSS and then tells me at the bottom that I don't have permission to access this resource. Because this is a live site I have made the menu link only available to registered users of which I am the only one. If someone needs to see this live, let me know offline and I will provide the URL, along with a username and password.
It would appear that your template's CSS files are being called in with absolute links rather than relative links. Call them in like this: <link rel="stylesheet" type="text/css" href="templates/dt_cms/css/template_css.css" /> This will solve the issue of no CSS being loaded. This is not an issue with DT Donate... it's SSL on your entire site. Try just the secure url ending in index.php. You'll see the same result. Get that working first before you try it with any components. Thanks.