What HD channels would I receive with a new HDTV and cable service but no receiver?

If the LCD has a QAM tuner then you will get some HD channels. In North American digital video, a QAM tuner is a device present in some digital televisions and similar devices which enables direct reception of digital cable channels without the use of a set-top box.[1] QAM-based HD programming of local stations is sometimes available to analog cable subscribers, without paying the additional fees for a digital cable box. The availability of QAM HD programming is rarely described or publicized in cable company product literature. If cable providers provide rebroadcasts of locally aired programming, they must also carry rebroadcasts of high-definition digital locally aired programming, in an unencrypted form, that does not require the customer to use leased equipment, per FCC Sec. 76.630 and CFR Title 47, §76.901(a). These usually include the local affiliates for CBS, NBC, ABC, PBS, and FOX, and the cable providers comply by rebroadcasting them over QAM channels. The law does not require the cable provider to advertise their availability, and the cable customer service representatives are known to unequivocally (and incorrectly) insist to customers that a converter box is mandatory to view any HD channels.

So where is this TV getting it's signal from, the cable system or your antenna? If cable, it's unlikely you'll get HD channels without having a cable box. In fact you may not even get all the normal standard definition channels as cable systems move towards compressing those digitally to make room for more HD channels. If you get the signal from the antenna, yes you should get some. Your new LCD will undoubtedly have an HD tuner built-in.