HP Pavilion a1610n will not boot up. I get the

You are probably installing a version of XP which is prior to service pack2.

Only SP2 or 3 will have the native drivers to get you machine functional, then you can use the HP motherboard drivers disk.

See the procedure on the microsoft website or other tecchie sites to SLIPSTREAM SP2 files on to your licensed SP1 disk and create a bootable copy.

If you have tried another monitor and result is the same, then it's a faulty graphics card.
If graphics card is sharing system memory, then you might need to replace ram to get it work again.