Hola @andres.tecnologia (Andrés) 
Soy portugués y aunque puedo leer y entender español, no puedo escribir en español. Así que esta respuesta mía fue escrita en inglés y traducida con la ayuda de "Google Translate". Esperemos que la traducción automática de Google no sea muy mala.
¡Creo que tengo buenas noticias para ti! Estoy escribiendo esta respuesta precisamente en un HP Pavilion dv6 de 12 años que ejecuta "Ubuntu MATE 22.10 (Kinetic Kudu)".
Las cosas que recuerdo que tuve que hacer para poder instalar Ubuntu MATE 22.10 en esta máquina fueron dos:
1 - "Grabe" el ISO (usando "Startup Disk Creator" = usb-creator-gtk) en una unidad flash USB que tenga al menos el tamaño de 8 GB. Me parece recordar que mis primeros intentos de arrancar el HP Pavilion dv6 desde el ISO grabado en una unidad flash de 4 GB, aunque el ISO estaba "ajustado", tuvieron varios problemas.
2 - Mencionas que, cuando intentas arrancar desde la unidad Flash, la pantalla se vuelve negra y no avanza. Pero ves un cursor parpadeante en la esquina superior izquierda, ¿verdad? Si ven eso, a mí también me pasó: el truco era simplemente esperar un largo tiempo (unos 10 minutos más o menos). Finalmente, el instalador se inicia.
¡Buena suerte! Por favor, responda de nuevo más tarde diciendo si funcionó para usted. En caso de que estés interesado, aquí están mis especificaciones:
$ inxi -ACDMNSG
System:
Host: hpavilhao Kernel: 5.19.0-23-generic arch: x86_64 bits: 64
Desktop: MATE v: 1.26.0 Distro: Ubuntu 22.10 (Kinetic Kudu)
Machine:
Type: Laptop System: Hewlett-Packard product: HP Pavilion dv6 Notebook PC
v: 049D210000241210000020000 serial: <superuser required>
Mobo: Hewlett-Packard model: 3659 v: 32.23 serial: <superuser required>
BIOS: Hewlett-Packard v: F.15 date: 01/05/2010
CPU:
Info: dual core model: Intel Core i3 M 330 bits: 64 type: MT MCP cache:
L2: 512 KiB
Speed (MHz): avg: 1436 min/max: 933/2133 cores: 1: 1463 2: 1379 3: 1463
4: 1439
Graphics:
Device-1: NVIDIA GT218M [GeForce G 105M] driver: nouveau v: kernel
Device-2: Suyin HP Integrated Webcam type: USB driver: uvcvideo
Display: x11 server: X.Org v: 1.21.1.4 driver: X: loaded: modesetting
unloaded: fbdev,vesa gpu: nouveau resolution: 1366x768~60Hz
OpenGL: renderer: NVA8 v: 3.3 Mesa 22.2.1
Audio:
Device-1: Intel 5 Series/3400 Series High Definition Audio
driver: snd_hda_intel
Device-2: NVIDIA High Definition Audio driver: snd_hda_intel
Sound Server-1: ALSA v: k5.19.0-23-generic running: yes
Sound Server-2: PipeWire v: 0.3.58 running: yes
Network:
Device-1: Broadcom BCM43225 802.11b/g/n driver: wl
Device-2: Realtek RTL8111/8168/8411 PCI Express Gigabit Ethernet
driver: r8169
Drives:
Local Storage: total: 223.57 GiB used: 11.78 GiB (5.3%)
ID-1: /dev/sda vendor: Kingston model: SA400S37240G size: 223.57 GiB
Here's my original text of this reply of mine in English:
Hi, @andres.tecnologia (Andrés)
I'm Portuguese and although I can read and understand Spanish, I can't write in Spanish. So this reply of mine was written in English and translated with the help of "Google Translate". Let's hope the automatic translation by Google is not very bad.
I think I have some good news for you! I'm writing this reply precisely in a 12 years old HP Pavilion dv6 running "Ubuntu MATE 22.10 (Kinetic Kudu)".
The things that I remember that I had to do to be able to install Ubuntu MATE 22.10 in this machine were two:
1 - "Burn" the ISO (using "Startup Disk Creator" = usb-creator-gtk) to an USB flash drive that has at least the size of 8 GB. I seem to remember that my early attempts of booting the HP Pavilion dv6 from the ISO burned to a 4 GB flash drive, although the ISO "fitted", had several problems.
2 - You mention that, when you try to boot from the Flash drive, the screen becomes black and doesn't advance. But you do see a blinking cursor in the upper left corner, right? If you see that, that also happened to me: the trick was simply to wait a long time (about 10 minutes or so). Eventually, the installer starts.
Good luck! Please reply again later telling if it worked for you. In case you're interested, here are my specs:
$ inxi -ACDMNSG
System:
Host: hpavilhao Kernel: 5.19.0-23-generic arch: x86_64 bits: 64
Desktop: MATE v: 1.26.0 Distro: Ubuntu 22.10 (Kinetic Kudu)
Machine:
Type: Laptop System: Hewlett-Packard product: HP Pavilion dv6 Notebook PC
v: 049D210000241210000020000 serial: <superuser required>
Mobo: Hewlett-Packard model: 3659 v: 32.23 serial: <superuser required>
BIOS: Hewlett-Packard v: F.15 date: 01/05/2010
CPU:
Info: dual core model: Intel Core i3 M 330 bits: 64 type: MT MCP cache:
L2: 512 KiB
Speed (MHz): avg: 1436 min/max: 933/2133 cores: 1: 1463 2: 1379 3: 1463
4: 1439
Graphics:
Device-1: NVIDIA GT218M [GeForce G 105M] driver: nouveau v: kernel
Device-2: Suyin HP Integrated Webcam type: USB driver: uvcvideo
Display: x11 server: X.Org v: 1.21.1.4 driver: X: loaded: modesetting
unloaded: fbdev,vesa gpu: nouveau resolution: 1366x768~60Hz
OpenGL: renderer: NVA8 v: 3.3 Mesa 22.2.1
Audio:
Device-1: Intel 5 Series/3400 Series High Definition Audio
driver: snd_hda_intel
Device-2: NVIDIA High Definition Audio driver: snd_hda_intel
Sound Server-1: ALSA v: k5.19.0-23-generic running: yes
Sound Server-2: PipeWire v: 0.3.58 running: yes
Network:
Device-1: Broadcom BCM43225 802.11b/g/n driver: wl
Device-2: Realtek RTL8111/8168/8411 PCI Express Gigabit Ethernet
driver: r8169
Drives:
Local Storage: total: 223.57 GiB used: 11.78 GiB (5.3%)
ID-1: /dev/sda vendor: Kingston model: SA400S37240G size: 223.57 GiB