I want to confirm this problem WinTV-HVR-1800 tuner card is not detected on DELL Tower 5810 PCIe bus.

It looks like that DELL team is not really concerned about this problem, since there is no reaction since Oct 2017.

It's time for Dell to start talking

This is generally a user to user forum so unless another customer has ran into this problem and solved it you might not get an answer.  The users who do work for Dell would only be able to answer questions on hardware that Dell has tested.  

PCI-E does not have the same BUS Speed, slot power or Line Code.   1.0 is not compatible with 2.0 and 3.0.

This is why Precision 490 690 workstations do not work with PCI-E 3.0 cards.

This is further complicated by secure boot and 64 bit windows 8 and 10 where directx 9 and 10 as well as windows media center is REMOVED.   This makes the cards ONLY work with windows VISTA or Windows 7.

Line code is replaced
1.0             8b/10b

3.0       128b/130b

This means the data is not readable and therefore cards in the bus are

NEVER seen.

There is also an incompatibility with older Conventional PCI cards where ONLY Universal 3.3v/5v cards work.   5v only cards with 1 keyway DO NOT WORK in Pentium 4 motherboards with PCI 2.2 Bus.

I use a pci hvr 1600 and usb hvr 1955 on 2 seperate machines.  I have tried wintv pci-e cards i do not like them.  But if u can get a hvr 1955 / 1950 they work on almost anthing that has a usb port,  I have had mine for about 1.5 years and not one problem with it.  It even has a fm radio tuner built in when using with wintv 8.

Maybe this will help maybe not.  My 1600 pci works in almost everything that had a pci slot.  The pci-e one i sold was not happy with hardly any machine i used it in.

The reason the HVR 1600 works is that its a UNIVERSAL Conventional PCI 2.2 card.  The system being complained about DOES NOT HAVE ANY PCI slots.

You can recognize these by the 2 keyways.  However The Media Software is required because they remove this with windows 8 NON MCE and 10 ALL versions.

wintv-hvr 1800  is an XP based Windows Media Center PCI-E 1.0 card and over 10 years old now.   Windows Media Center is REMOVED from Windows 8 non MCE and removed altogether from all versions of windows 10.   Windows Media center Directx 9 and Directx 10 in Home Premium, Ultimate, Professional and Enterprise editions of Windows XP/Vista/7. This card will work in ancient Dell Precision 490 or 690.

So although the card is supported the HARDWARE is not supported in PCI-E bus 3.0.  This is not a Dell issue. Any WinTV 7 application CD can be used during the install. If you do not have your original WinTV CD-ROM but would like to update to WinTV v7 or WinTV v8, you can purchase a new CD on the Hauppauge webstore for $9.95

http://www.hauppauge.com/site/support/support_hvr1800a.html?zoom_highlight=windows+10

And also for about $100.00 you can get the hvr 1955 which is a nice usb tuner.  thats my daily driver , use it with comcast cable box.  The 1600 is used for atsc broadcast watching in hd .