Problem Using USBTinyISP

I'm trying to upload an application, WITHOUT the bootloader, to a custom board using a USBTinyISP, but there seems to be a problem, and I don't know if it's hardware problem with the board, something I'm doing wrong, or just a configuration problem. The part is a 328P, and it programs and functions perfectly using the Serial port and bootloader. But, when attempting to program using the USBTinyISP, it fails, with the following output:

...
Sketch uses 4440 bytes (14%) of program storage space. Maximum is 30720 bytes.
Global variables use 248 bytes (12%) of dynamic memory, leaving 1800 bytes for local variables. Maximum is 2048 bytes.
E:\Users\RayL\Documents\AppData\Arduino\arduino-1.8.9\hardware\tools\avr/bin/avrdude -CE:\Users\RayL\Documents\AppData\Arduino\arduino-1.8.9\hardware\tools\avr/etc/avrdude.conf -v -patmega328p -cusbtiny -Uflash:w:C:\Users\RayL\AppData\Local\Temp\arduino_build_502767/sketch_aug21a.ino.hex:i 

avrdude: Version 6.3-20171130
         Copyright (c) 2000-2005 Brian Dean, http://www.bdmicro.com/
         Copyright (c) 2007-2014 Joerg Wunsch

         System wide configuration file is "E:\Users\RayL\Documents\AppData\Arduino\arduino-1.8.9\hardware\tools\avr/etc/avrdude.conf"

         Using Port                    : usb
         Using Programmer              : usbtiny
avrdude: usbdev_open(): Found USBtinyISP, bus:device: bus-0:\\.\libusb0-0001--0x1781-0x0c9f
         AVR Part                      : ATmega328P
         Chip Erase delay              : 9000 us
         PAGEL                         : PD7
         BS2                           : PC2
         RESET disposition             : dedicated
         RETRY pulse                   : SCK
         serial program mode           : yes
         parallel program mode         : yes
         Timeout                       : 200
         StabDelay                     : 100
         CmdexeDelay                   : 25
         SyncLoops                     : 32
         ByteDelay                     : 0
         PollIndex                     : 3
         PollValue                     : 0x53
         Memory Detail                 :

                                  Block Poll               Page                       Polled
           Memory Type Mode Delay Size  Indx Paged  Size   Size #Pages MinW  MaxW   ReadBack
           ----------- ---- ----- ----- ---- ------ ------ ---- ------ ----- ----- ---------
           eeprom        65    20     4    0 no       1024    4      0  3600  3600 0xff 0xff
           flash         65     6   128    0 yes     32768  128    256  4500  4500 0xff 0xff
           lfuse          0     0     0    0 no          1    0      0  4500  4500 0x00 0x00
           hfuse          0     0     0    0 no          1    0      0  4500  4500 0x00 0x00
           efuse          0     0     0    0 no          1    0      0  4500  4500 0x00 0x00
           lock           0     0     0    0 no          1    0      0  4500  4500 0x00 0x00
           calibration    0     0     0    0 no          1    0      0     0     0 0x00 0x00
           signature      0     0     0    0 no          3    0      0     0     0 0x00 0x00

         Programmer Type : USBtiny
         Description     : USBtiny simple USB programmer, https://learn.adafruit.com/usbtinyisp
avrdude: programmer operation not supported

avrdude: Using SCK period of 10 usec
avrdude: AVR device initialized and ready to accept instructions

Reading | ################################################## | 100% 0.00s

avrdude: Device signature = 0xffffff (probably .avr8x_mega) (retrying)

Reading | ################################################## | 100% 0.00s

avrdude: Device signature = 0xffffff (probably .avr8x_mega) (retrying)

An error occurred while uploading the sketch
Reading | ################################################## | 100% 0.01s

avrdude: Device signature = 0xffffff (probably .avr8x_mega)
avrdude: Yikes!  Invalid device signature.
         Double check connections and try again, or use -F to override
         this check.


avrdude done.  Thank you.

The table of information printed near the start of the upload suggests it CAN talk to the 328, but later on it cannot get the device ID, usually returning either 0x000000, 0xffffff, or 0x0000ff. Basically the same thing happens when I attempt to re-write the bootloader.

Am I doing something wrong, or is there a problem with this chip?

Regards, Ray L.

The table of information printed near the start of the upload suggests it CAN talk to the 328, but later on it cannot get the device ID, usually returning either 0x000000, 0xffffff, or 0x0000ff. Basically the same thing happens when I attempt to re-write the bootloader.

The first information just tells which parameters were supplied to avrdude. So you did tell it that it's connected to an ATmega328p but when it tries to get the identification from the processor that already fails. This usually means that the connection to the ICSP connector is not working. You either did connect the wrong pins or some of the wires are broken. Check every single wire and then try again. If unsure about the wiring, post sharp pictures showing the connections clearly. We might find the error.