The /OE pin is often just connected to the CPU /READ line or derived from the READ /WRITE signal, depending on the CPU and hardware setup.
You need to look at the chip enable signals - and all of them in combination, on a device such as this that has several - to know if it is really being accessed.
/OE has no effect unless the device is also enabled.
Edit: Only pin B4 enable is actually relevant in your board as the other enables are tied to a pullup resistor, if the diagram you posted is for that board.
You don't say what type of computer board it is.
If the ROM is the only only program storage for the system it will be continuously accessed anyway, as Pommie says.
If it's supposed to be displaying something or booting from other media, it may be stuck in a loop waiting for whichever peripheral to be connected or become ready.
If it's a PC board of some sort, do you have a speaker / sounder directly connected to it, to hear any error code beep signals it may be producing?
A BIOS diagnostic card - aka "POST Card" - is also very useful for faultfinding with problems such as that; many PC BIOSs will output status codes to an I/O port as they go through the stages of the hardware testing and boot sequence & those status codes can be viewed with a simple plug-in card that has a LED or LCD display.
This ebay listing illustrates various versions for different PC bus types:
Find many great new & used options and get the best deals for 2/4 Digit 3 in1 PCI-E PC Analyzer Analysis Diagnostic USB Card POST Card TOP at the best online prices at eBay! Free delivery for many products.
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Beep codes list, if the board has a speaker connection:
More about the POST card numeric codes:
A POST code is a hexadecimal code generated by a computer motherboard's BIOS during the POST. View one with a POST test card.