It has USB ports(?) and whatever comes with hp pavilion 6735.
This is your motherboard.

This is the layout of your motherboard.

1 - COM 2 connector
2 - CPU fan connector
3 - CPU socket 370
4 - 82810-DC100
5 - DIMM sockets
6 - RTC battery 15
7 - PS fan connector
8 - Power connector
9 - Floppy drive connector
10 - IT8702
11 - Speaker
12 - IDE connectors
13 - JP-6 clear CMOS
14 - Front panel connector
15 - 82802AP (ROM)
16 - 82801AA
17 - CD-ROM connector
18 - PCI slots
As you can see through the layout you only have 3 regular PCI slots. Some graphical processors the are designed for PCI-Express (PCI-E) can be socketed in a regular PCI slot. Quite a few of them do not support this.
Put in short: It's really necessary that you have a PCI-E slot on your computer if you want to install a graphical processor that is at least powerful.
If you want you can
research Graphical Processors that still support regular PCI.
Also going to point out that you're motherboard still only supports IDE for Disc drives and hard drives... ouch...