Hi Joseph
I once replied to this message but I now have a lot more information and there is a chance that we connect. It is unlikely that we connect on the Nardulli line because they came from Mola (Giaconto was born in Mola in 1852 and married Maria Tommasini in Triggiano on May 24 1875) and I have almost nothing in Mola.
I have a bunch of marriages of your clan in my marriage spreadsheet. I got some of it from looking in other towns and some from Santa Maria Addolorata Chirch in Chicago where all my relatives went.
I have marriage dates for 5 sons and one daughter of Giacinto Nardulli and Maria Tommasini.
Tommaso Nardulli (born 1880) married Maria Picicco (born 1881 in Capurso) on May 18 1905 in Capurso.
Francesco Nardulli (born 1876) married Maria Lorita Roppo (born 1877 in Ceglie del Campo) on Sep 18 1902 in Ceglie.
Pasquale Nardulli (this must be your grandfather) married Maria Mancuso? (born in Montemaggiore Belsito?) on Oct 18 1908 in Chicago (presumably SMA)
Michele Nardulli married Anna Rosso (of Chicago) on Mar 19 1911 in Chicago (SMA)
Vincenzo Nardulli (born 1882) married Vita Maria Pavone (born 1886 in Triggiano) on Apr 8 1905 in Triggiano.
Annunziata Nardulli (born 1890) married Tommaso Barruffi (born 1884 in Capurso) on Oct 30 1910 in Triggiano.
Maria Tommasino was daughter of Tommaso and Vincenza Giampietro, who married Jul 1 1854 in Triggiano. Tommaso was son of Vito and Maria Losapio. Vincenza was daughter of Domenico and Rosa Mallardi. I do connect to Rosa Mallardi.
The problem with all of this is that the brothers you listed don't match all the ones I'm finding. Are you sure Pasquale's father was Giacinto? The one in my marriage record is definitely the son of Giacinto and Maria Tommasino.
Please check what you have against what I wrote here and lets see if we're on the same page. If we are we'll take it from there.
Thanks
Dan Niemiec