Connecting Dell 3020 to TV

Post back the spec of your Displaypot to HDMI cable.

https://blogs.msdn.microsoft.com/danchar/2014/10/07/displayport-hdmi-dongles-active-vs-passive-re-visited/

Not all displayport to hdmi cable are created equal, you need one which are active adapter if you want to solve your problem. Of course, active adapters are more expensive than passive ones.

Most of today's TV's will "autosense" which input is active and use it automatically.  Have you tried switching the TV manually to use the HDMI port from the Dell?

Thanks for your responses,
The cable a bought was a cheap one off ebay:
http://www.ebay.co.uk/itm/272106153727
I have tried switching TV inputs, turning on and off and re-connecting the HDMI cable at the back of the TV and the only thing that works is reconnecting the Displayport connector at the back of the PC.
I am considering getting an active adaptor or a DVI/graphics card for the PC but not sure which one would be compatible?
Thanks again,Tom

Apparently, displayport comes in several flavors with only one of them, dual-mode, working with HDMI and what must be causing your issue is that the PC doesn't redetect the monitor (TV) type when it wakes up.  Why it doesn't use the same setting it was using when it went to sleep is a different question, altogether.
In order to help you further, I really need the service tag number for the Dell which will let me see the specifics of your PC?
BTW, I don't think you need an active adapter cable.  If you did, it wouldn't ever work.

Yes what you say about the active adaptor makes sense as after I reconnect the cable it works perfectly.
The service tag is 8RZ9302.
Thanks.

The latest BIOS is version A14 from last November and newer BIOS' are usually released to fix problems.  You might want to try that:
http://www.dell.com/support/home/us/en/04/Drivers/DriversDetails?driverId=PXGWH&fileId=3583640735&osCode=W732&productCode=optiplex-3020-desktop&languageCode=en&categoryId=BI
The support page shows both the small desktop and the mini tower.  Which do you have?

I think you pasted it into wrong window.... You can ask your computer vendor to support cheap converter for 10 year old TV.... Probably it will not get better than you have it.

I already ran the Dell driver update software and installed the latest A14 BIOS update.
I have the small version SFF.
Thanks

You can compare an active and passive displayport to hdmi adapter in term of price.

Active
https://www.amazon.co.uk/LINDY-DisplayPort-HDMI-Adapter-Cable/dp/B00R4NIUD0

Passive
https://www.amazon.co.uk/Kabalo-DisplayPort-MALE-LAPTOP-ADAPTOR-x/dp/B017JFN55U

What is the brand / model of your TV?

It is a Toshiba 40BV801B - quite an old one...

I think you are right - I will probably just get a video card. Not fussed about games so just a basic one will do.
I previously had the TV connected to my old PC with a DVI-HDMI cable and it worked fine so I may get a DVI card for the Dell.
I found this cheap one readily available on ebay:

http://www.ebay.co.uk/itm/Dell-FH868-0FH868-Sil-1364A-ADD2-N-PCI-Express-DVI-D-Low-Profile-Adapter-Card-/310745155633?hash=item4859dac831:g:jk4AAOSwcu5UQMBq

My PC is not on the compatibility list but is there any reason why it would not work?
thanks

That makes sense. Please excuse my ignorance, I am new to graphics cards!

I would consider the one you recommend but would like to spend as little as possible.
Would you say the GT 710 is the most suitable for my system? There is a slightly cheaper version on ebay...

http://www.ebay.co.uk/itm/Low-Profile-Palit-NVIDIA-GeForce-GT-710-1GB-Graphics-Card-VGA-DVI-HDMI-/182102546547?hash=item2a66285873:g:dKcAAOSwYudXGk7B

That one should work just fine!
The Manuals link on your support page will tell you how to open your Dell and install it:
http://www.dell.com/support/home/us/en/19/product-support/servicetag/8RZ9302/diagnose

Thanks for all your help!

You're welcome.

I am being asked to close this question; did you get it resolved?

I'm glad you got it working!

Answered as confirmed by author.