OptiPlex 7040 BIOS update failed

Here is the Dell BIOS recovery procedures.  One of these may help.

How to Recover the BIOS on a Dell Computer or Tablet | Dell US

If you are still not able to recover, here is the Dell Policy on a failed BIOS update:

Dell Policy, BIOS breaks motherboard CMOS

In warranty customers

If a Dell Support representative directs you to update the BIOS, and it broke the motherboard CMOS, Dell will replace the motherboard.
Stipulations =
* The service itself could be either onsite service or Return to Dell Depot, depending on which warranty you purchased

If you updated the BIOS without any direction from a Dell Support representative, and it broke the motherboard CMOS, Dell will do a one time only motherboard replacement.
Stipulations =
* The service itself could be either onsite service or Return to Dell Depot, depending on which warranty you purchased
* We will then ask you to not install any BIOS update unless you contact us first and have us guide you

Out of warranty customers

If a Dell Support representative directs you to update the BIOS, and it broke the motherboard CMOS, you are eligible for a one time only out of warranty motherboard replacement.
Stipulations =
* This is a one time only offering
* This is a parts only service. Dell will not send on onsite technician
* Dell will only have motherboards available for 5 years from the original system RTS (Ready To Ship) date. If you are past this 5 year period, you will need to purchase the motherboard from a 3rd party seller

If you updated the BIOS without any direction from Dell Support representative, and the BIOS update broke the motherboard CMOS, you have to buy the replacement motherboard either from Dell or a 3rd party seller.

I've run through everything on that page. I guess this one is destined for the bin frustratingly, as it is out of warranty. I'll try calling Dell in the week in case they are able to suggest anything further. 

Replace the CMOS battery if it hasn't been done within the last 5 years.  A low battery will cause all sorts of bizarre seemingly unrelated problems, including boot/boot loop issues.

Good shout on the BIOS battery. I don't think it's that (as it isn't getting that far) but it is worth a shot. 

It's a SFF 7040, looking on eBay replacement boards start around the £70 mark. I didn't want to go down that route as for not much more you can pick up an entire machine. I'm Dell certified through work though so replacing the board won't be much hassle. 

Please don't forget to let us know how it goes.

I'd definitely try the battery first (cheap).  Better deals on Energizer and Duracell on Amazon than in store, at least in the U.S. anyway.

If by chance that doesn't work, remember to keep the battery, especially if you get refurb or used.

Replacing the battery has had successes before, so hopefully it works for you.

A new battery hasn't changed anything, looks like this machine is toast. 

We manage thousands of OptiPlex's at work and I've never seen one like this before. Thanks for everyone's suggestions

7040SFF Dell PN is HD5W2.  If you wait you may get a good deal some day on ebay.  currently £42.21.  https://www.ebay.co.uk/itm/Dell-OptiPlex-7040-SFF-Desktop-Motherboard-Mainboard-LGA1151-HD5W2/233301293501?hash=item3651d739bd:g:nscAAOSwbbtdQNtF

Thanks. Including postage I suspect that will be a similar price to uk listings. I'll keep an eye out for them.