When installing a signed driver (i.e. with a properly signed .CAB) on Windows 7 through DpInst, unless it's a WHQL-signed driver, you cannot install it silently. If you run DpInst in the non-silent mode, it'll prompt you to trust the "publisher". If you run DpInst in silent mode, it would fail with a signing-related error code (something like 0x800b0109 -- check your setupapi.app.log).
While ilya's answer is good, the solution on Windows 7 is even easier. The command below deploys the certificate to both the current user and the system trusted publisher certificate stores. It requires administrative privileges and is provided by Microsoft.
certutil.exe -addstore TrustedPublisher cert.cer
I verified that this works on Windows 7 64-bit to deploy signed, but not WHQL-certified, drivers - without prompting the user.
It appears that on XP you still need to have the drivers WHQL-certified in order to avoid prompts on install.
For Windows XP you'll need to download the Windows Server 2003 Admin Tools Pack from Microsoft and extract certutil.exe and certadm.dll. Then the command above will work on XP as well.
Admin Tools Pack: http://www.microsoft.com/download/en/details.aspx?DisplayLang=en&id=16770
Note that the extracted msi file can be inspected by 7-zip, so you don't need to install it to obtain the exe and dll you need.