Hi Mike, sorry to hear about the non booting issues.
it doesn't sound too good, but I guess you don't need me to tell you that….. 
The main clue from your post is that you are receiving a checksum error and that usually means the problem exists even before Windows starts to load.
The check sum is similar to a number that is resident in the BIOS chip (on the motherboard) and when you switch on the machine this number is checked and if there is a mismatch then you receive the error you have been getting and the computer won't start. The BIOS also has a small (usually 3v) battery to power it and if this battery runs down too far, it can cause problems although does not normally prevent the machine from booting up.
(it is a replaceable item….often it's a CR 2032 its 20mm in diameter and 3.2mm in depth…hence the name 2032) it's about the sign of a coin, 5p, nickel, etc., bright and shiny in appearance.usually has a life of around 5 years or so but can last twice as long, or fail after only a few months (rare but it does happen.) it only costs a pound or so, or a dollar or two and is easy to replace on a desktop computer but more tricky on a laptop, especially some makes of laptop that require a complete strip down to get at it! Some laptop manufactures are very "kind" to us repair shop owners and provide us with a good source of income by making what should be a 5 minute job to perform, take around an hour or so!
The end point voltage (no load) is around 2.8v
The first thing to check is to see if you can get into the BIOS and if you can then make a note of all the settings and then reset it to "default" ….. it's important to make a note of all the settings so you can put things back as they were if it should be necessary….. this making a note of them is tedious, time consuming, and some folks don't bother doing it…… This can render your machine a doorstop (prevent it from working) so failing to make a note is a risky procedure…. 
The owners manual from the manufacturer or the Motherboard maker will help here.
As your machine is running Win 8.1 it's possible (likely even) that your BIOS is called UEFI or it may be called "set up" or CMOS……
If you can reset the BIOS. .we'll keep calling it that for the purpose of this topic, this should be the first step….. then try a reboot with all peripherals removed, printers network cables, cameras, cards, phones, etc.all disc drives empty, no memory sticks inserted, and with just a hard wired keyboard and mouse (not wireless or bluetooth) power connection and VDU (if its its a desktop computer) and nothing else at all connected.
if no joy then replace the battery CR2032.
if still no joy then you may be looking at a replacement motherboard and these together with fitting are expensive, very expensive…. so you may need to get a quote from a repair shop for you to see if the machine is capable of economic repair or whether it should be "recycled" and you start with a new one..
Regards
paws
