It is really important to read the DOT rule before contacting any carrier, including TP, or complaining to DOT. Those who do not, are risking their access to an important tool.
The mandatory 24-hour cancellation applies to all US and foreign carriers serving the US and in the case of foreign carriers, for tickets marketed through a website marketed to US consumers. It does not apply if one books through a third-party, e.g. a travel agent or on a website not marketed to US customers. In addition, the burden to cancel in a timely manner is on the consumer. Make certain that you follow any call with an email or similar web form and that you retain a time-stamped copy unless you have a written confirmation from the carrier that is has cancelled and initiated a refund. If you are offered a voucher, make it clear that you want a refund and confirm that in your email (webform). Remember that other timing requirements apply.
In the event that you have complied with the Rule, both a chargeback and a DOT Complaint are in order. Easiest to do them at the same time with the same backup paper. Make certain that you supply the backup paperwork (from above) with your chargeback and DOT Complaint. This would include your e-ticket receipt showing the date & time, as well as your request for cancellation. If your chargeback "packet" is complete, it is harder for the merchant acquirer to put together a negative response and furthermore, when confronted with clear evidence, they may well not bother to respond at all.
On the good side, all of the US carriers have more generous policies than required by law.