I have been upgrading my collection of working timetables, so for a number of years from 1973 to 1981 (with the exception of the 1977-1978 timetable which I don't have) the SX service from Hartford to Warrington and beyond was the following, and only in 1980 did it get even vaguely interesting.
None of the (few) services went via Newton-le-Willows.
Clearly there wasn't much demand but the service on offer wasn't going to generate demand either.
Hartford had a few other calls in fast Liverpool services, but not many.
Summer Saturdays saw a couple of additional DMU services to Blackpool North.
7/5/73 to 5/5/74 SX
1P16 09:28 Crewe-Carlisle D280 called at Hartford, Warrington Bank Quay, Wigan North Wester, Preston & onwards
1K17 18:03 Carlisle-Crewe D280 called at ..., Preston, Wigan North Western, Warrington Bank Quay, Hartford, arrived Crewe 20:46
6/5/74 to 4/5/75 SX (first year of electrification)
2P82 09:17 Crewe-Preston/Carnforth EMU called at Hartford, Warrington Bank Quay, Wigan North Western & Preston, arrived 10:10, 1/7 to 27/9 departed unadvertised 10:28 to Carnforth arrive 10:51
2K82 15:00 Preston-Crewe EMU called at Wigan North Western, Warrington Bank Quay, Hartford, arrived Crewe 15:54
5/5/75 to 2/5/76 SX
1P82 09:17 EMU Crewe-Preston called at Hartford, Warrington Bank Quay & Wigan North Western, arrived Preston 10:10
1K82 15:00 Preston-Crewe EMU called at Wigan North Western, Warrington Bank Quay, arrived Crewe 15:54
(1K82 didn't call at Hartford)
3/5/76 to 1/5/77 SX
2P66 09:17 EMU Crewe-Preston called at Hartford, Warrington Bank Quay & Wigan North Western, arrived Preston 10:13
2K66 14:57 EMU Preston-Crewe EMU called at Wigan North Western, Warrington Bank Quay, Hartford, arrived Crewe 15:53
2/5/77 to 7/5/78 SX
I don't have this timetable, so I don't know
8/5/78 to 13/5/79 SX
no services
14/5/79 to 11/5/80 SX
no services
12/5/80 to 10/5/81 SX
1P16 06:28 Birmingham-Lancaster E280 called at Crewe 07:35, Hartford, Warrington Bank Quay, Wigan North Western & Preston, arrived Lancaster 08:47 (stock formed 2P92 09:20 Lancaster-Barrow-in-Furness D280, LD from Preston after working 1S45 07:53 Manchester Victoria-Glasgow Central as far as Preston)
1P63 16:05 Crewe to Barrow-in-Furness E280 to Preston called at Hartford, Warrington Bank Quay, Wigan North Western, Preston 16:55-17:05, Lancaster, Carnforth & onwards
1K34 12:50 Preston-Crewe E280 called at Wigan North Western, Warrington Bank Quay, Hartford, arrived Crewe 13:41
1K32 14:10 Barrow-in-Furness-Crewe E280 from Preston called at stops to Carnforth, Lancaster, Preston 15:37-15:50, Wigan North Western, Warrington Bank Quay, Hartford, arrived Crewe 16:40
EDIT I have a feeling that I might have travelled on 1K34 or 1K32 once, because I remember calling at Hartford on something which wasn't the stopping Liverpool-Crewe EMU service (and I only used that the once), and I remember having a nice AC-hauled journey from Preston to Crewe one afternoon, maybe in the summer before going to university? The dates would work.