[CentOS] Old hardware, newer kernels

I have an old server (old hardware) that's been running 6.4 with kernel
2.6.32-279.19.1.el6.i686, no problem.  Except, any kernel update after that
causes it not to boot anymore.  All I get is a blinking cursor on the
screen, nothing else.

Is this the end of this hardware, no more kernel updates after this?

For reference, these are all the options that kernel is booting up with
(lines wrapped on purpose):

title CentOS (2.6.32-279.19.1.el6.i686)
        root (hd0,0)
        kernel /boot/vmlinuz-2.6.32-279.19.1.el6.i686 ro \
           root=UUID=3f79e6b6-7845-499f-b708-aef782602673 rd_NO_LUKS
rd_NO_LVM \
           rd_NO_MD rd_NO_DM LANG=en_US.UTF-8 SYSFONT=latarcyrheb-sun16 \
           KEYBOARDTYPE=pc KEYTABLE=us noapic apm=off ide=nodma acpi=off \
           crashkernel=auto rhgb quiet selinux=0
        initrd /boot/initramfs-2.6.32-279.19.1.el6.i686.img