If your battery is dying it could be the old 850 glove compartment warped door problem that keeps the light on. Normally this doesn't do any major drainage damage unless the battery is old, the car sits for a while or you only take short trips.

You can eliminate the fuel pump relay from consideration by jumpering it out of the circuit.

Remove the relay (#103) and look next to the pins in the base. Molded into the plastic you should see the numbers 31, 31b, 15, and 87. Fashion a jumper wire and jumper between the socket connections that correspond to pins 15 and 87. If the car fires right up your relay is bad. If it still doesn't run then you may or may not have a problem with the pump. The only way to tell for sure is with a fuel pressure gauge.

If the pump and regulator is working properly you should see 43.5 PSI at the end of the rail.

...Lee

I'll concur with the other responses about the battery. In this area, anyway, most auto parts stores will test the battery for free - though it's only ethical then to buy your battery from them, so pick a store whose battery you'll like. I've found NAPA batteries are pretty decent, actually, for instance. Get this right first. Some auto parts stores will even roll a charging system tester out to your car and test the charging system for free or cheap; again, they expect that you'll buy any needed parts from them, but the extra cost may be worth your while over blind gambling on parts.

If you don't already own one of the fix-your-Volvo books, like Haynes, buy one; though I have to say that the Haynes 850 book is a major disappointment. Far less useful information than their books on earlier cars. Your local library will also have Chilton manuals for cars. In one of those, you should be able to find the wiring information that tells you which wires going into the relay are the switching wires (operate the relay) and which are the switched wires. Try first jumping the switching wires, once you know, and see if the relay operates. If it doesn't, this is probably your problem. If not, then it's either the pump or a wiring problem.

Low-voltage situations can reveal weakness in your circuitry, and so, oddly, can do you a favor, especially if you live in the colder parts of the country (where the car's under more stress when the thermometer's down into single digits or negative digits, and where you REALLY don't want to walk home if it fails on you at night). If you've got a voltage drop due to corrosion, failing wire, etc., somewhere in the system, it may operate OK when the system is just brimful of volts and amps, but fail when things are marginal. There's no better approach to finding voltage drops than testing each connection through the circuit, looking for the weak point. I once spent a day and a half (when I was younger and, I like to think, dumber) trying to figure out why the fuel pump on my 1973 145 wasn't working before I traced the entire circuit, finding that the ground wire to the pump was loose and the connection rusty. A little sandpaper and a new sheet metal screw later, it ran just fine.

If your battery keeps failing, check your battery and/or alternator. If the battery is 5 or more years old, get a new one. Check the output of the alternator, it should put out at least 14.7 volts. It may need new brushes.

When you turn the key to pos II, before you engage the starter, do you hear any noise? The fuel pump should humm for a second or 3.
Yes, there is a way to "jump" the relay, and I apologize for not writing down which 2 pins get jumped. Try searching the web.

Klaus
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The 164 has a new home, all I am left with are a 95 854T and a 98 V70R :)

What makes you think that the low voltage (I'll get to that is a second) is causing a fuel problem? Did you install a fuel pressure gauge when the car doesn't start? Knowing the ACTUAL pressure is the only way to know if this is the problem or not.

Now to the low voltage. A good battery that is being properly charged, and not drained when the car is off will NOT have low voltage. It sounds as if this is the true cause of your starting troubles.