I have a 1995 Bonneville SE 3800
227K miles

I have what I think is an electrical problem.
The problem is intermittent.
When I turn the key to the ON position, the fuel pump ususally pumps
for 2 seconds then stops.  Sometimes, instead I hear the fuel relay
under the glove box go crazy and the relay under the hood go crazy with
clicking.  In this case the fuel pump clicks on and off continuously.
While the relays are going nuts the car won't start, or will stall
immediately after starting.  Feels like a fuel starvation issue.  The
engine turns fine, just no start or a quick stall.

I tested the relays.  They are good.  The problem may continue for
several minutes, and I'll occasionally get 3 fast chimes from the
instrument cluster.  Eventually the I get lucky and the clicking stops,
the fuel pump runs for 2 secs and I get 3 final chimes from the
instrument panel.  Then everything runs fine.  The CEL is OFF, so there
are no codes to pull.

This problem can also happen while I'm driving at high or low speeds.
I'll get a loss of power and eventually stall.

A funny thing I can't seem to tie into this is that the speedometer
(analog) goes up when I turn the key ON and the clicking is happening.
I don't understand this.  It also happens when the car is getting ready
to stall out while driving, the speedometer goes way up to 90 or 100+,
even though I'm going much slower...

I've replaced the fuel filter.
Fixed a vaccum leak.
New plugs/wires.

Any help will be greatly appreciated.  Let me know if you need more
info too.  I'm not sure what's wrong - my current guesses include:

Wiring problem - possible intermittent ground issue?  I'll visually
inspect wiring, but some is kind of hidden - where should I look
specifically?
Faulty computer - This will cost me $100 to replace and there's no
returns...  Is there a way to test the computer first?
Fuel pump - Is there an easy way to test this?  What's the normal
current draw for a pump?  It could be the pump is intermittently
failing, shorting and drawing too much current, which causes the relays
to go crazy??

Can anyone help me further diagnose the problem?

Thanks!