First, your last line of code is wrong. It looks like you are trying to get the Test to which the Test Config belongs. "testConfig.ID" is accessing the ID property of a TestConfig object. That is the ID of the Test Config object, not the ID of the associated test case. If you want the associated test case, then you need to use the TestId property of the TestConfig object.
What version of QC are you using? While it is true that there are no direct method or properties to extract some of the Test Config information, there are other ways to get at it. You mentioned the test parameters. In v11, there is an additional interface supported for the TestConfig object - the ISupportParameterValues. It looks like that would help you get the parameter information.
In general, if there isn't a property or method specific to the data you want, but you know the database field name then you can use the Field property to get the value from any field in the database table associated to the object. Refer to the Database Reference documentation for more information on the database table schemas.
According to the Database Reference, depending on the source of the parameter values they may be stored in either the TEST_PARAMS table or the ASSET_RELATIONS table. You may need to access different objects to get the data.
(Opinions and information contained in this post are wholly my own and do not reflect the opinions of my employer.)