Just to clarify...
There are three specific NMEA 0183 sentences which can be used to provide the bare minimum position information needed for the HP-1 to know where it is and whether the GPS is locked onto the satellites:
$GPGGA - Global Positioning System Fix Data
GGA,123519,4807.038,N,01131.324,E,1,08,0.9,545.4,M,46.9,M, , *42
123519 Fix taken at 12:35:19 UTC
4807.038,N Latitude 48 deg 07.038' N
01131.324,E Longitude 11 deg 31.324' E
1 Fix quality: 0 = invalid
1 = GPS fix
2 = DGPS fix
08 Number of satellites being tracked
0.9 Horizontal dilution of position
545.4,M Altitude, Metres, above mean sea level
46.9,M Height of geoid (mean sea level) above WGS84
ellipsoid
(empty field) time in seconds since last DGPS update
(empty field) DGPS station ID number
$GPGLL - Geographic position, Latitude and Longitude
GLL,4916.45,N,12311.12,W,225444,A
4916.46,N Latitude 49 deg. 16.45 min. North
12311.12,W Longitude 123 deg. 11.12 min. West
225444 Fix taken at 22:54:44 UTC
A Data valid
(Garmin 65 does not include time and status)
$GPRMC - Recommended minimum specific GPS/Transit data
RMC,225446,A,4916.45,N,12311.12,W,000.5,054.7,191194,020.3,E*68
225446 Time of fix 22:54:46 UTC
A Navigation receiver warning A = OK, V = warning
4916.45,N Latitude 49 deg. 16.45 min North
12311.12,W Longitude 123 deg. 11.12 min West
000.5 Speed over ground, Knots
054.7 Course Made Good, True
191194 Date of fix 19 November 1994
020.3,E Magnetic variation 20.3 deg East
*68 mandatory checksum
Any or all of these 3 sentences contain the latitude and longitude in degrees and decimal minutes, the North, South, East or West indicator and whether or not the data is valid. If the HP-1 can hear and understand any one of these sentences then it should know where it is.
There's nothing in the spec that I've been able to discover which gives an option for position format. For example you cannot comply with NMEA 0183 if your GPS sends latitude and longitude as either decimal degrees or as degrees minutes and seconds. Only degrees and decimal minutes fully complies with the NMEA 0183 spec since none of the 3 position sentences have any way of indicating what the format should be. It must be assumed that the latitude and longitude will be a string of digits broken down into degrees and minutes with a decimal point in the minutes value.
It's true that many GPS pucks natively support some proprietary data format other than NMEA 0183. It's assumed that the owner knows this and can set the format to NMEA 0183 before using the GPS with the HP-1 as the HP-1 does not send any configuration strings to the GPS.
As to the green light being lit, that can only indicate that valid NMEA sentences containing the GPS status are being received. If the LED is red, no data is being received. If yellow it's receiving valid sentences but the GPS status is still listed as invalid. Green indicated both valid GPS sentences and a valid data indicator in whichever NMEA 0183 sentence it's using.
I want to help, not prove myself as some sort of expert (which I'm not). I didn't get the impression that the O.P. was getting the green status indicator. If so, then there truly could be some sort of error either in his GPS or in the HP-1's software. There's no reasonable explanation for the green GPS indicator unless the unit is sending NMEA 0183 sentences. They're pretty unique and cannot be easily confused with other formats. For example, for the $GPRMC sentence to be decoded with a valid fix it must contain at a minimum "$GPRMC,,A,,,,,,(checksum)" so there must be some data coming from the GPS that's considered valid. The other two sentences ($GPGGA and $GPGLL) don't require the checksum but have even more stringent requirements for data to be seen as valid since the validity indicator us buried further down the data stream.
I just don't see the probability of getting a green GPS status indicator unless one of these 3 sentences is being correctly decoded, so that (in my opinion) rules out most proprietary data formats. It does, however, leave the possibility of a defective GPS or a flaky data connection.
It also, unfortunately, leaves the possibility that the GPS knows where it is but cannot find any in-range channels due to either the remoteness of the location, bad data from RadioReference.com or a bad data upload from Sentinel to the HP-1. I might recommend a hard-reset of the HP-1 and/or formatting and reloading the SD card if it's suspected that the data may be corrupt.
With that huge data-dump; I'm done. Fix it or don't fix it matters not to me as mine works correctly. I'm just trying to help diagnose the problem and keep everyone from speculating without the needed background data.