Can't see it start.

redux 1;
PC found on road dead, a FORD. (no day1 media from maker)
so put linux on it end story but that big battery needs to be taken out, and the RTC coin cell is no good at all at 15 year sold.
Some of these old PCs have odd duck RTC batteries.
oops that is what is there, i SEE IT . ON BOTTOM CORNER.
If BIOS acts odd ( cant keep time or date in BIOS page)
or cant save settings and not scramble them this RTC chargeable batter is no good,or needs 24 hour charge per manual.

XP is a virus magnet, so we can skip that.
PC was sold in 2003, 15 years
https://www.manualslib.com/manual/180201/Toshiba-Satellite-M35-Series.html?page=90&term=recovery&selected=1

boot this
http://www.pcdied.com/linux.html

restar the computer HOLD the key CTRL +F2 and ready.

God bless you

It appears that the issue might be with some hardware malfunctions. It may happen due to hardware failure, BIOS mismatch or due to
static charge. Let us try the basic troubleshooting. Turn Off the
Computer, remove all the devices attached to the computer, the power
cable and battrey, now holdon the power button for 15 secs (make sure
adpater and battery are uplugged) it will drain out all the static
charge. Now, restart the computer and keep on tapping F2, you will enter
to BIOS setup utility, press F9 (click "Yes", if you are prompted) and
then press F10 (Click "Yes", if you are prompted), it will restart the
computer. If still it is not booting to normal mode, then we have to
perform a full system recovery & it is a distructive process as you will
loose all the datas on the computer. To do so, Turn Off the computer,
now as soon as you hit the power button, keep on holding "Alt" key &
keep on tapping "F10" key, i.e Alt+f10, it will open the recovery
console, select full factory restore and follow onscreen instruction.
NOTE: This will erase all the datas on the computer

Reconnect the old monitor.
Start Windows.
Right-mouse click anywhere on your "wallpaper".
Click Properties.
Click Settings.
Move the slider to 800-by-600 or 1024-by-768.
Click Apply
In 'Advanced', set the refresh-rate to 60 Hertz.
Click OK.
Shutdown.
Reconnect the new monitor.
Restart your computer.
Right-mouse click anywhere on your "wallpaper".
Click Properties.
Click Settings.
Now try moving the slider to higher values.
If the screen goes blank, wait 15 seconds, and Windows will cancel your change to a higher value.

The problem is that UBUNTU is setting the screen-resolution to some values that your monitor does not support, e.g., 1920-by-1080, or not setting it to 60Hz.

During boot-up, your monitor uses 800-by-600, so it "initially" works, both with UBUNTU and XP.

Windows "detects" the monitor, and selects "usable" settings.

Attach a new monitor to UBUNTU, and then set the video-resolution to 1024-by-768 and to 60 Hz -- your Compaq should support those settings.

Sounds to me like the input has gone out of the boundaries the monitor supports. IE the refresh rate is too high frequency (normally 60 to 72 Hertz for LCD's) or the screen resolution has been set too high.

Go into safe mode and set it back to 1024 X 768 at a frequency of 60 Hz, once back into windows proper you can try higher resolutions and change your refresh, if the screen goes black or displays a message "Out of Bounds" or similar it should revert after 15 seconds if left alone.

Have fun

Sounds like something that installed recently isn't playing nice with Windows, two things to try:

1. When you boot up, hit the F8 key repeatedly till you get to a menu, select Last Known Good Configuration, and see if that let's the computer come up.
2. If you installed any hardware or peripherals recently, unplug or uninstall them from the computer physically and see if you can start back up.
   

Hmm... Any errors on the screen?

Could be a power supply. Fluctuations in that can cause power drops, which would be visible in the video card, and if severe enough, cause the PC to shut off. There are 4 screws and one 1 wire holding those in. It would take about 10 minutes to replace and probably cost you $40-$50 in parts.

To have Geeks do it: Probably $100.