English t/d are not quite palatal, nor are they dental. Rather, they lie between the two, being articulated around the alveolar ridge. English t lies somewhere between the Sanskrit cerebral TH (or T, depending on phonological context) and dental th (or t).
In English, the letter `t' (likewise `p' and `k') is usually aspirated when appearing in syllable-initial position; in many European (and other) languages it is not. To speakers of English, an unaspirated `t' sounds much like `d'; this is, for example, the reason the Pinyin transcription system (used to romanise Chinese) represents an unaspirated voiceless dental stop as `d' rather than `t'.
On an somewhat-related note, `t' (and sometimes `d') at the end of a syllable often becomes a glottal stop. So, for example, in many English dialects (especially in the U.S. and ``lower class'' England) `button' is pronounced `bu-n', and `cut' becomes `cu-'. There may be some alveolar co-articulation involved, but often there is not.